Question

Verify the identity.

cos(x+pi/2) = -sinx

Answer 1

see explanation

Explanation:

Using the cosine addition identity

cos(x + y) = cosxcosy - sinxsiny

and cos(
`(\pi )/(2)`) = 0, sin(
`(\pi )/(2)`) = 1

cos(x +
`(\pi )/(2)`)

= cosxcos(
`(\pi )/(2)`) - sinxsin(
`(\pi )/(2)`)

= cosx × 0 - sinx × 1

= 0 - sinx

= - sinx