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