Question

How do you prove `sin (x- (pi/2))= cos x`?

Answer 1

The right hand side should be `- cos x`
Expand `sin(x-pi/2)` using `sin(a-b)=sin a cos b-cos a sin b`.

Explanation:

Prove `sin (x-pi/2 )=-cos x`.

Using `sin(a-b)=sin a cos b-cos a sin b`,
`sin (x-pi/2)=sin x cos (pi/2)-cos x sin (pi/2) = 0- cos x`.