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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
In an acute-angled triangle ABC, `tanA+tanB+tanC`A. `ge3`B. `gesqrt3`C. `ge3sqrt3`D. none of these |
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Answer» Correct Answer - C In `DeltaABC,` we have `tanA +tanB+tanC=tanAtanBtanC" "...(i)` But, `A.M geG.M.` `implies(tanA+tanB+tanC)/(3)ge(tanAtanBtanC)^(1//3)` `implies((tanAtanBtanC)/(3))ge(tanAtanBtanC)^(1//3)" "["Using(i)"]` `implies((tanAtanBtanC)/(3))^(2//3)ge1` `impliestanAtanB tanCge3^(3//2)` `tan A tanBtanCge3sqrt3` |
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| 2. |
If an angle `theta` is divided into two parts A and B such that `A-B=x `and `tanA :tanB=k :1`, then the value of sinx isA. `(K-1)/(K-1)sinalpha`B. `(k)/(k+1)sinalpha`C. `(k-1)/(k+1)sinalpha`D. none of these |
| Answer» Correct Answer - C | |
| 3. |
If `sinA+sinB=(pi)/(4),then (tanA+1)(tanB+1)` is equal toA. 1B. 2C. `sqrt3`D. `-1` |
| Answer» Correct Answer - B | |
| 4. |
If `cosA=tanB, cos B=tanC, cosC=tanA,` then sin A is equal toA. `sin 180^(@)`B. `2sin18^(@)`C. `2cos18^(@)`D. `2 cos36^(@)` |
| Answer» Correct Answer - B | |
| 5. |
The expression `(tanA)/(1-cota)+(cosA)/(1-tanA)` can be written asA. `sinA cos A+1`B. `sec A coses A+1`C. `tanA+cot A`D. `sec A+cosec A` |
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Answer» Correct Answer - B `(tanA)/(1-cotA)+(cotA)/(1-tanA)` `=(sin^(2)A)/(cos A(sinA-cosA))+(cos^(2)A)/(sinA(cosA-sinA))` `=(sin^(3)A-cos^(3)A)/(sinA cos A (sinA-cosA))` `=(1+sinA cosA)/(sinA cosA(sinA-cosA))` `=(1+sinAcosA)/(sinA cos A)=sec A cosec A+1` |
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| 6. |
The radius of the circle whose are of length `15 pi`cm makes an angle of `3pi//4`radius at the centre is`10 c m`b. `20 c m`c. `11 1/4c m`d. `22 1/2c m`A. `10 cm`B. `20 cm`C. `11(1)/(4)cm`D. `22(1)/(2)cm` |
| Answer» Correct Answer - B | |
| 7. |
If `(cosA)/(cosB)=n and (sinA)/(sinB)=m,then (m^(2)-n^(2))sin^(2)B=`A. `1-n^(2)`B. `1+n^(2)`C. `1-n`D. `1+n` |
| Answer» Correct Answer - A | |
| 8. |
If A is an obtause angle, then `(sin^(3)A-cos^(3))/(sinA-cosA)+(sinA)/(sqrt(1+tan^(2)A))-2tanA cotA.` is always equal toA. 1B. `-1`C. 2D. none of these |
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Answer» Correct Answer - B We have, `(sin^(3)A-cos^(3)A)/(sinA-cosA)+(sinA)/(sqrt(1+tan^(2)A))-2tanA cotA.` `=(sin^(2)A+cos^(2)A+sinAcosA)+(sinA)/(|secA|)-2` `=1+sinA cosA-sinA cosA-2=-1.` |
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| 9. |
If n is an odd positive interger, then `((cosA+cosB)/(sinA-sinB))^(n)+((sinA+sinB)/(cosA-cosB))^(n)=`A. `-1`B. 1C. 0D. none of these |
| Answer» Correct Answer - C | |
| 10. |
The value of `sin pi/n + sin (3pi)/n+ sin (5pi)/n+...` to n terms is equal toA. 1B. 0C. `n/2`D. none of these |
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Answer» Correct Answer - B We know that `sin alpha+sin(alpha+beta)+...+sin{alpha+(n-1)beta}` `=(sin{alpha+(n-1)(beta)/(2)}sin((n beta)/(2)))/(sin""(beta)/(2))` `thereforesin""(pi)/(n)+sin""(3pi)/(n)+sin""(5pi)/(n)+....` to n terms `=(sin{(pi)/(n)+(n-1)(pi)/(n)}sin((npi)/(n)))/(sin((pi)/(n)))" "[Here, alpha =(pi)/(n)and beta=(2pi)/(n)]` `=(sinpui sin pi)/(sin""(pi)/(n))=0` |
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| 11. |
`sum_(r=0)^(n) sin^(2)""(rpi)/(n)` is equal toA. `(n+1)/(2)`B. `(n-1)/(2)`C. `n/2`D. none of these |
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Answer» Correct Answer - C We have, `underset(r=0)overset(n)(sum)sin^(2)""(rpi)/(n)` `=1/2underset(r=0)overset(n)(sum){1-cos""(2rpi)/(n)}` `=1/2underset(r=0)overset(n)(sum)1-1/2underset(r=0)overset(n)(sum)cos""(2rpi)/(n)` `=((n+1))/(2)-1/2{1+cos""(2pi)/(n)+cos""(4pi)/(n)+...+cos""(2npi)/(n)}` `=((n+1))/(2)-1/2{cos""(4pi)/(n)+cos""(6pi)/(n)+...+cos""(2(n-1)pi)/(n)}` `=((n-1)/(2))=1/2xx(cos pisin(pi-(pi)/(n))=(n-1)/(2)+1/2=n/2` |
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| 12. |
If `cosA+cosB=m` and `sinA+sinB=n` then `sin(A+B)=`A. `(mn)/(m^(2)+n^(2))`B. `(2mn)/(m^(2)+n^(2))`C. `(m^(2)+n^(2))/(2mn)`D. `(mn)/(m+n)` |
| Answer» Correct Answer - B | |
| 13. |
If `ltA lt(pi)/(6) and sinA+cosA=(sqrt7)/(2),"then" tan""(A)/(2)=`A. `(sqrt7-2)/(3)`B. `(sqrt7+2)/(3)`C. `(sqrt7)/(3)`D. none of these |
| Answer» Correct Answer - A | |
| 14. |
The value of `cospi/11+cos(3pi)/11+cos(5pi)/11+cos(7pi)/11+cos(9pi)/11` is |
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Answer» Correct Answer - C We known that `cos alpha+cos(alpha+beta)+cos(alpha+2 beta)+...+cos{alpha+(n-1)beta}` `=(cos{alpha+(n-1)(beta)/(2)}sin((nbeta)/(2)))/(sin""(beta)/(2))` `thereforecos""(pi)/(11)+cos""(3pi)/(11)+cos""(5pi)/(11)+cos""(7pi)/(11)+cos""(9pi)/(11)` `=(cos((pi)/(11)+(4pi)/(11))sin((5pi)/(11)))/(sin((pi)/(11)))" "[because alpha=(pi)/(11)and beta=(2pi)/(11)]` `=(cos""(5pi)/(11)sin""(5pi)/(11))/(sin""(pi)/(11))=1/2(sin""(10pi)/(11))/(sin""(pi)/(11))=1/2.` |
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| 15. |
If `x=tan15^(@),y=cosec75^(@),z=4sin18^(@)`A. `xltyltz`B. `yltzltx`C. `zltxlty`D. `xltzlty` |
| Answer» Correct Answer - A | |
| 16. |
`(1+cos.(pi)/(8))(1+cos.(3pi)/(8))(1+cos.(5pi)/(8))(1+cos.(7pi)/(8))` is equal toA. `1/2`B. `cos""(pi)/(8)`C. `1/8`D. `(1+sqrt2)/(2sqrt2)` |
| Answer» Correct Answer - C | |
| 17. |
`cos^(4)theta-sin^(4)theta` is equal toA. `1+2sin^(2)""(theta)/(2)`B. `2cos^(2)theta-1`C. `1-2sin^(2)""(theta)/(2)`D. `1+2cos^(2)theta` |
| Answer» Correct Answer - B | |
| 18. |
For all values `of theta,3-costheta+cos(theta+(pi)/(3))` lie in the intervalA. `[-2,3]`B. `[-2,1]`C. `[2,4]`D. `[1,5]` |
| Answer» Correct Answer - C | |
| 19. |
The value of `sin pi/16 sin (3pi)/16 sin (5pi)/16 sin (7pi)/16` isA. `(sqrt2)/(16)`B. `1/8`C. `1/6`D. `(sqrt2)/(32)` |
| Answer» Correct Answer - A | |
| 20. |
The value of `sin(pi/14)sin((3pi)/14)sin((5pi)/14)` isA. 1B. `1//4`C. `1//8`D. `sqrt2//7` |
| Answer» Correct Answer - C | |
| 21. |
If `(sin^(4)theta)/(a)+(cos^(4)theta)/(b)=(1)/(a+b),` then which one ofhte following is incorrect?A. `(sin^(4)theta)/(a^(2))=(cos^(4)theta)/(b^(2))`B. `(sin^(4)theta)/(b^(2))=(cos^(4)theta)/(a^(2))`C. `(sin^(8)theta)/(a^(3))+(cos^(8)theta)/(b^(3))=(1)/((a+b)^(3))`D. `sin^(4)theta=(a^(2))/((a+b)^(2))` |
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Answer» Correct Answer - B We have, `(sin^(4)theta)/(a)+(cos^(4)theta)/(b)=(1)/(a+b)` `(a+b)((sin^(4)theta)/(a)+(cos^(4)theta)/(b))=(sin^(2)theta+cos^(2)theta)^(2)` `impliessin^(4)theta+cos^(4)theta+b/asin^(4)theta+a/bcos^(4)theta` `" "=(sin^(4)theta+cos^(4)theta+2sin^(2)thetacos^(2)theta)` `(sqrt((b)/(a))sin^(2)theta-sqrt((a)/(b))cos^(2)theta)^(2)=0` `impliessqrt((b)/(a))sin^(2)theta=sqrt((a)/(b))cos^(2)theta` `impliesbsin^(2)theta=acos^(2)theta` `implies(sin^(2)theta)/(a)=(cos^(2)theta)/(b)=(sin^(2)theta+cos^(2)theta)/(a+b)` `impliessin^(2)theta=(a)/(a+b)and cos^(2)theta=(alpha)/(a+b)` Clearly, these values satisfy options (a), (c ) and (d) only. Hence, option (b) is incorrect. |
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| 22. |
Which of the following statement is incorrectA. `sin theta=-1//5`B. `cos theta=1`C. `sec theta=1//2`D. `tantheta=20` |
| Answer» Correct Answer - C | |
| 23. |
The minimum value of the expression `sin alpha + sin beta+ sin gamma`, where `alpha,beta,gamma` are real numbers satisfying `alpha+beta+gamma=pi` isA. positiveB. zeroC. negativeD. `-3` |
| Answer» Correct Answer - A | |
| 24. |
If `A+B+C=270^@` , then `cos2A+cos2B+cos2C+4sinAsin B sinC=` |
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Answer» Correct Answer - B We have, `cos2A+cos2B+cos2C+4sinAsinBsinC` `=2cos(A+B)cos(A-B)+cos2C+4sinA sinBsinC` `=2cos((3pi)/(2)-C)cos(A-B)+cos2C+4sinA sinBsinC` `=-2sinCcos(A-B)+1-2sin^(2)C+4sinAsinBsinC` `=-2sinC{cos(A-B)+sinC}+4sinAsinBsinC+1` `=-sinC{cos(A-B)-cos(A+B)}+4sinAsinBsinC+1` `=-4sinAsinBsinC+4sinA sinBsinC+1=1` |
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| 25. |
If `tanalpha=sqrta` where a is not a perfect square then which of the following is a rational numberA. `sin 2 alpha`B. `tan 2 alpha`C. `cos 2 alpha`D. none of these |
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Answer» Correct Answer - C We have, `sin2 alpha=(2tanalpha)/(1+tan^(2)alpha)=(2sqrta)/(1+a),` which is an irrational number `tan2alpha=(2 tanalpha)/(1-tan^(2)alpha)=(2sqrta)/(1-a),` which is an irrational number `cos 2 alpha=(1-tan^(2)alpha)/(a+tan^(2)alpha)=(1-a)/(1+a),` whihc is a rational number. |
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| 26. |
If `cos^(3)x sin2x=sum_(n=1)^(n) a_(m)sinmx` is an identity in x, then which one of the following is in-correct?A. `a_(2)=0,a_(3)=3/8`B. `a_(1)=1/2,n=6`C. `a_(1)=1/4, n=5`D. `suma_(m)=3/4` |
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Answer» Correct Answer - B We have, `cos^(3)x sin2x=((cos3x+3 cosx)/(4))sin2x` `impliescos^(3)x sin2x=1/4(sin2x cos3x+3sin2xcosx)` `impliescos^(3)x sin2x=1/8(sin2x cos 3x+6sin2x cosx)` `impliescos^(3)x sin2x=1/8(sin 5xsinx+3 sin3x+3sinx)` `thereforecos^(3)x sin2x=underset(m=1)overset(n)(sum)a_(n)sin mx` `impliesa_(1)sinx+a_(2)sin2x+...+a_(n)sinnx` `=1/4sinx+3/8sin 3x+1/8sin5x` `impliesa_(1)=1/4,a_(2)=0,a_(3)=3/8,a_(4)=0,a_(5)=1/8` |
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| 27. |
Which one of the following number (s) is/are rational?A. `sin15^(@)`B. `cos15^(@)`C. `sin15^(@)cos15^(@)`D. `sin15^(@)cos75^(@)` |
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Answer» Correct Answer - C We have, `sin 15^(@)=sin(45^(@)-30^(@))=(sqrt3-1)/(2sqrt2)` `impliessin15^(@)=1/4(sqrt6-sqrt2),` whichis an irrational number `sin 15^(@)cos 15^(@)=1/2sin 30^(@)=1/4,` which a rational number `sin 15^(@)cos 75^(@)=sin^(2)15^(@)=1/2(1-cos30^(@))=(2-sqrt3)/(4)` which is an irrational number. |
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| 28. |
Len n be an odd integer. If `sinn theta=sum_(r=0)^(n) b_(r)sin^(r)theta` for every value of `theta,` thenA. `b_(0)=1, b_(1)=3`B. `b_(0)=0, b_(1)=n`C. `b_(0)=-1, b_(1)=n`D. `b_(0)=0, b_(1)=n^(2)-3n+3` |
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Answer» Correct Answer - B We have, `sinn theta=underset(r=0)overset(n)(sum)b_(r)sin^(r)theta"for all"theta.` Putting `theta=0,` we get ` 0=b_(0)` Again, `sinn theta=underset(r=0)overset(n)(sum)b_(r)sin^(r)theta` `implies(sinntheta)/(sintheta)=underset(r=0)overset(n)(sum)b_(r)(sintheta)r^(r-1)` `impliesunderset(6to0)(lim)(sinntheta)/(sintheta)=underset(r=1)overset(n)(sum)b_(r)underset(thetato0)(lim)(sintheta)^(r-1)` `impliesn =b_(1)` Hence`,_(0)=0and b_(1)=n` |
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| 29. |
If `tanx=b/athen sqrt((a+b)/(a-b"))+sqrt((a-b)/(a+b))=`A. `(2sinx)/(sqrtsin2x)`B. `(2cosx)/(sqrtcos2x)`C. `(2cosx)/(sqrtsin2x)`D. `(2sinx)/(sqrtcos2x)` |
| Answer» Correct Answer - B | |
| 30. |
The maximum and minimum values of `-4le5cos theta+3cos(theta+(pi)/(3))+3le10` are respectivelyA. 5B. 10C. 11D. `-11` |
| Answer» Correct Answer - B | |
| 31. |
The interior angles of a polygon are in AP The smallest angle is `120` and the common difference is 5. Find the number of sides of the polygon.A. 9 or 16B. 9C. 13D. 16 |
| Answer» Correct Answer - B | |
| 32. |
Let `f : (-1, 1) -> R` be such that `f(cos4theta) = 2/(2-sec^2theta` for `theta in (0, pi/4) uu (pi/4, pi/2)`. Then the value(s) of `f(1/3)` is/areA. `1+-(sqrt3)/(2)`B. `1+-sqrt((2)/(3))`C. `1+-sqrt((1)/(3))`D. `1+-sqrt((1)/(2))` |
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Answer» Correct Answer - A If `0in(0,(pi)/(4))uu((pi)/(4),(pi)/(2)), then 2thetain(0, (pi)/(2))uu((pi)/(2),pi)` Therefore, `cos 2 theta` can be positive or negative. Hence, `cos2theta=pmsqrt((1+cos4theta)/(2))` `impliescos 2theta=pmsqrt((1+(1)/(3))/(2))=+-sqrt((2)/(3))" "["Taking"cos4theta=1/3]` Now, `f(cos4theta)=(2)/(2-sec^(2)theta)=(2cos^(2)theta)/(2cos^(2)theta-1)=(1+cos2theta)/(cos2theta)` `impliesf((1)/(3))=1+-sqrt((3)/(2)). [because cos4theta=1/3and cos2theta=+-sqrt((2)/(3))]` |
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| 33. |
If `(cos theta)/(a)=(sintheta)/(b), then (a)/(sec 2 theta)+(b)/(cosec 2 theta)` is equal toA. aB. bC. `a/b`D. `a+b` |
| Answer» Correct Answer - A | |
| 34. |
If `y=(sin 3theta)/(sintheta), theta nen pi, ` thenA. `y in[-1,3]`B. `y in(-oo,-1]`C. `y in(3,oo)`D. `y in[-1,3)` |
| Answer» Correct Answer - D | |
| 35. |
Statement-1: The numbers `sin18^(@)and-sin54^(@)` are the roots of the quadratic equation with integer coefficients. Statement-2: If `x=18^(@),cos3x=sin2x and If y=-54^(@), sin2y =cos 3y.`A. Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement -1.B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False, Statement-2 is True. |
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Answer» Correct Answer - A Clearly, statement-2 is true Using statement-2, we have `cos 3x=sin2x` `impliescos^(3)x-3cosx=2 sinxcosx` `implies4(1-sin^(2)x)-3=2sinx` `implies4sin^(2)x+2sinx-1=0` `impliessinx=sin18^(@)` is a root of a quadratic equation with integer coefficients. Similarly, ` sinty=cos3y` `impliessiny=sin(-54^(@))=-sin54^(@)` are the roots of a quadratic equation with integer coefficients. |
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| 36. |
Statement-1: If `2sin""(theta)/(2)=sqrt(1+sintheta)+sqrt(1-sintheta,) then theta in((8n+1)(pi)/(2),(8n+3)(pi)/(2))` Statement-2: `If""(pi)/(4)lethetale(3pi)/(4),then sin""(theta)/(2)gt0.`A. Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement -1.B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False, Statement-2 is True. |
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Answer» Correct Answer - B We have, `2sin""(theta)/(2)=sqrt(1+sintheta)+sqrt(1-sintheta)` `implies2sin""(theta)/(2)=sqrt((cos""(theta)/(2)+sin""(theta)/(2))^(2))+sqrt((cos""(theta)/(2)-sin""(theta)/(2))^(2))` `implies2sin""(theta)/(2)=|cos""(theta)/(2)+sin""(theta)/(2)|+|cos""(theta)/(2)-sin""(theta)/(2)|` `rArr "cos"(theta)/(2) + "sin"(theta)/(2)gt0 and "cos"(theta)/(2)-"sin"(theta)/(2) lt0` `rArr sin ((pi)/(4)+(theta)/(2)) gt0 and cos ((theta)/(2)+(pi)/(4))lt0` `rArr 2n pi +(pi)/(2)lt(0)/(2)+(pi)/(4)lt2n pi+pi` `implies(8n+1)(pi)/(2)lt thetalt(8n+3)(pi)/(2)` So, statement-1 is true. Statement-2 is also true, but it is not a correct explanation for Statement-1. |
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| 37. |
If `theta` lies in the second quadrant, then the value `sqrt(((1-sintheta)/(1+sintheta)))+sqrt(((1+sintheta)/(1-sintheta)))`A. `2 sec theta`B. `-2sec theta`C. `sec theta`D. `-sec theta` |
| Answer» Correct Answer - B | |
| 38. |
If `theta` lies in the first quadrant which of the following in not trueA. `(theta)/(2)lttan ((theta)/(2))`B. `(theta)/(2)ltsin ""(theta)/(2)`C. `thetacos^(2)((theta)/(2))ltsintheta`D. `theta sin"(theta)/(2)lt 2 sin""(theta)/(2)` |
| Answer» Correct Answer - B | |
| 39. |
If A lies in the third quadrant and `3 tan A-4 = 0,` then `5 sin 2A + 3sinA + 4 cosA` is equal to |
| Answer» Correct Answer - A | |
| 40. |
A and B are positive acute angles satisfying the equations `3cos^(2)A+2cos^(2)B=4and (3sinA)/(sinB)=(2cosB)/(cosA),then` A+2B is equal toA. `(pi)/(3)`B. `(pi)/(2)`C. `(pi)/(6)`D. `(pi)/(4)` |
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Answer» Correct Answer - B We have, `(3sinA)/(cosA)=(2cosB)/(cosA)` `implies(3sinA)/(cosA)=(2cosB sinB)/(cos^(2)A)` `impliestanA=1/3(sin2B)/(cos^(2)A)` `impliestanA=1/3tan2B.(cos2B)/(cos^(2)A)` `impliestanA=1/3(tan2B)/(cos^(2)A)(2cos^(2)B-1)` `impliestanA=1/3(tan2B)/(cos^(2)A)(4-3cos^(2)A-1)" "[{:(,because2cos^(2)B),(,=4-3cos^(2)A):}]` `impliestanA=tan2Btan^(2)A` `impliestanA tan2B=1` `impliestanA =cot2B` `impliestanA=tan((pi)/(2)-2B)` `impliesA=(pi)/(2)-2BimpliesA+2B=(pi)/(2)` |
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| 41. |
The value of `sin""(pi)/(7)sin""(2pi)/(7)sin""(3pi)/(7),` isA. `1//8`B. `sqrt7//8`C. `sqrt7//8`D. `sqrt7//16` |
| Answer» Correct Answer - B | |
| 42. |
The value of `sin""(2pi)/(7)+sin""(4pi)/(7)+sin""(8pi)/(7),` isA. `sqrt7//8`B. `1//8`C. `sqrt7//2`D. `-sqrt7//2` |
| Answer» Correct Answer - C | |
| 43. |
If `T_(n)=cos^(n)theta+sin ^(n)theta, then 2T_(6)-3T_(4)+1=`A. 2B. 3C. 0D. 1 |
| Answer» Correct Answer - C | |
| 44. |
The expression `tan^2alpha+cot^2alpha` isA. `ge2`B. `ge2`C. `ge-2`D. none of these |
| Answer» Correct Answer - A | |
| 45. |
Let ` cos (alpha+beta) = 4/5` and `sin(alpha-beta)=5/13 ` where `0 |
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Answer» Correct Answer - D We have, `cos(alpha+beta)=4/5and sin(alpha-beta)=5/13`n `impliestan(alpha+beta)=3/5and tan(alpha-beta)=15/12` `thereforetan 2alpha=tan(alpha+beta+alpha-beta)=(tan(alpha+beta)+an(alpha-beta))/(1-tan(alpha+beta)tan(alpha-beta))` `impliestan 2alpha=((3)/(5)+(5)/(12))/(1-(3)/(5)xx(5)/(12))=56/33` |
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| 46. |
The set of all poddible ualuse of `alpha` in `[-pi,pi]` such that `sqrt((1-sinalpha)/(a+sinalpha))` is equal to sec `alpha-tanalpha,` isA. `[0,pi//2)`B. `[0,pi//2)uu(pi//2,pi)`C. `[-pi,0]`D. `(-pi//2,pi//2) |
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Answer» Correct Answer - C Clearly, `sec alpha-tan alpha` is not difined for `alpha=+-pi//2.` Now, `sqrt((1-sinalpha)/(1+sinalpha))=sqrt(((1-sinalpha)^(2))/(cos^(2)alpha))` `impliessqrt((1-sinalpha)/(a+sinalpha))=(1-sinalpha)/(|cosalpha|)=sec alpha-tanalpha,if cos alphagt0` Clearly, `cos alphagt0impliesalphain(-pi//2,pi//2)` |
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| 47. |
If `alpha and beta` be between `0 and (pi)/(2)and if cos(alpha+beta)=(12)/(13) and sin(alpha-beta)=3/5,` then sin 2 `alpha` is equal toA. `64//65`B. `56//65`C. 0D. `16//15` |
| Answer» Correct Answer - B | |
| 48. |
If `alpha+beta=pi/2` and `beta+gamma=alpha` then `tanalpha` equalsA. `2(tanbeta+tangamma)`B. `tanbeta+tangamma`C. `tan beta+2 tangamma`D. `2tanbeta+tangamma` |
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Answer» Correct Answer - C We have, `beta+gamma+alpha` `impliesgamma=alpha=beta` `tangamma=tan(alpha-beta)` `impliestangamma=(tanalpha-tanbeta)/(1+tanalphatanbeta)` `impliestangamma=(tanalpha-tanbeta)/(1+tanalphacot alpha)" "[becausealpha+beta=(pi)/(2)becausebeta=(pi)/(2)-alpha]` `impliestangamma=1/2(tangamma-tanbeta)impliestanalpha=tanbeta+2tangamma.` |
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| 49. |
If `cos(alpha+beta)=4/5, sin(alpha-beta)=5/13and alpha, beta` between 0 `and (pi)/(4),then tan 2 alpha=`A. `56/33`B. `33/56`C. `16/65`D. `60/61` |
| Answer» Correct Answer - A | |
| 50. |
The value of `tan20^(@)+2 tan50^(@)-tan70^(@),` isA. 1B. 0C. `tan50^(@)`D. none of these |
| Answer» Correct Answer - B | |