Question

I need to find the identity of this equation for pre calc ​

Answer 1

Expand the left side using the angle sum identity for sine:

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

cos(π/2) = 0 and sin(π/2) = 1, so the right side reduces to

sin(x + π/2) = cos(x)

as required.