Prove the identity sin 2 2 Solutionsin pi2 x sin pi2 x

Prove the identity.

Solution

sin ( pi/2 - x) = sin ( pi/2 + x)

manipulating left hand side

sin (pi/2 - x) = cos x

sin pi/2 cos x - cos pi/2 sin x = cos x

and also

sin (pi/2 + x) = sin pi/2 cos x + cos pi/2 sin x

= cos x

so, left side is equal to right side

hence proved !