InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If `A+B+C=pi` then prove that `cos^2 (A/2)+cos^2 (B/2)-cos^2 (C/2)=2cos(A/2)cos(B/2)sin(C/2)` |
|
Answer» We have `LHS=cos^(2)""(A)/(2)+cos^(2)""(B)/(2)-cos^(2)""(C)/(2)` `=(1)/(2)(1+cosA)+(1)/(2)(1+cosB)-(1)/(2)(1+cos C)` `=(1)/(2)+(1)/(2)(cosA+cos B-cos C)` `=(1)/(2)+(1)/(2)[(4cos""(A)/(2)cos""(B)/(2)sin""(C )/(2))-1]` `=2 cos ""(A)/(2)cos""(B)/(2)""sin""(C)/(2)=2cos ""(A)/(2)cos""(B)/(2)sin""( C)/(2).` |
|