Verify the identity.

sin (x+pi/2) = cos x

Given data

sin (x+pi/2) = cos x

now using sin law

sin (a+b) = sin (a) cos (b) + cos (a) sin (b)

now using above values

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

as we know that

sin (pi/2) = 1

cos (pi/2) = 0

now putting these values

sin (pi/2+x) = 1*cosx+0*1

sin (pi/2+x) = cosx

hence proved that

sin (x+pi/2) = cos x