Verify the identity. sin quantity x plus pi divided by two = cos x

Question

Precalculus

Answer 1

Kenneth gave you a good answer.  Here is another way, using the identity

 

sinθ = cos(π/2 - θ)

 

and the property

 

cos(-x) = cos(x).

 

Let θ = x + π/2

 

Then

 

sin(x + π/2) = cos[π/2 - (x + π/2)] = cos(-x) = cos(x)

 

Answer 2

sin(x+pi/2) = sin x cos (pi/2) + cos x sin (pi/2) = (sin x)(0) + (cos x)(1) = cos x using angle-sum formula for sine.