Question

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

Answer 1

see below

Explanation:

cos ( x+pi/2) = -sinx

We know that

cos(A + B) = cos A cos B - sin A sin B

Let x = A and pi/2 = B

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

We know cos pi/2 = 0 and sin pi/2 = 1

cos x * 0 - sin x *1 = -sin x

- sin x = - sin x