Question

Cos^2 a/2-sin^2 b/2 =

Answer 1

LHS=cos 2 A+cos 2 B+2cosAcosB+sin 2 A+sin 2 B−2sinAsinB

(cos 2 A+sin 2 A)+(cos 2 B+sin 2 B)+2cosAcosB−2sinAsinB

2+2cosAcosB−2sinAsinB

2+cos(A+B)+cos(A−B)−cos(A−B)+cos(A+B)

2+2cos(A+B)   (∴cosx=2cos 2 x/2 - 1)

2+2 [2cos 2 (A+B)/2 −1  

2+4 cos 2 (A+B)/2 −2=4cos 2 (A+B)/2  =R.H.S

Hence proved