If `sinA sinB sinC+cosAcosB=1,` then the value of sinC isA. 1B. `1//2` – InterviewSolution

InterviewSolution

1.	If `sinA sinB sinC+cosAcosB=1,` then the value of sinC isA. 1B. `1//2`C. 0D. `-1`
Answer» Correct Answer - A `As cos C le1` `therefore sinA sinB sinC+cosAcosB lesin A sinB+cosA cosB` `impliessin A sinBsinC+cosAcosBlecos(A-B)` `implies1lecos(A-B)` `impliescos(A-B) =1impliesA=B` `thereforesinA sinBsinC+cosAcosB=1` `impliessin^(2)A sinC+cos^(2)A=1` This is satisfied by `sin C =1` only.

Discussion

No Comment Found

Related InterviewSolutions

In an acute-angled triangle ABC, `tanA+tanB+tanC`A. `ge3`B. `gesqrt3`C. `ge3sqrt3`D. none of these
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
If `sinA+sinB=(pi)/(4),then (tanA+1)(tanB+1)` is equal toA. 1B. 2C. `sqrt3`D. `-1`
If `cosA=tanB, cos B=tanC, cosC=tanA,` then sin A is equal toA. `sin 180^(@)`B. `2sin18^(@)`C. `2cos18^(@)`D. `2 cos36^(@)`
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`
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`
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`
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
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
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