Related InterviewSolutions

• 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-sqrt((3)/(2))`B. `1+sqrt((3)/(2))`C. `1-sqrt((2)/(3))`D. `1+sqrt((2)/(3))`
• Given `alpha+beta+gamma=pi,`prove that `sin^2alpha+sin^2beta-sin^2gamma=2sinalphasinbetacosgammadot`
• If A + B + C = `180^(@)`, then prove that tan A + tan B + tan C = tan A tan B tan C.
• prove that : `tan(alpha)+2 tan(2alpha) +4(tan4alpha)+8cot(8alpha) = cot(alpha)`
• If tan A = `(1-cos B)//sinB`, then tan 2A = tan B.
• In any triangle ABC prove that `cot(A/2)+cot(B/2)+cot(C/2)=cot(A/2)cot(B/2)cot(C/2)`
• If the lengths of the sides of a triangle are in AP and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle isA. `3 : 4 : 5`B. `4 : 5 : 6`C. `5 : 9 : 13`D. `5 : 6 : 7`
• If `A >0,B >0a n dA+B=pi/3,`the maximum value of `tanAtanB`is______
• The value of sin `10^(@)` sin `30^(@)` sin `50^(@)` sin `70^(@)` isA. `(1)/(36)`B. `(1)/(32)`C. `(1)/(16)`D. `(1)/(18)`
• If `A = sin^2 theta+ cos^4 theta`, then for all real values of `theta`A. `1leAle2`B. `(3)/(4) le A le 1`C. `(13)/(16) le A le 1`D. `(3)/(4) le A le (13)/(16)`