Question

How do you verify the identity `cos(pi/2+x)=-sinx`?

Answer 1

use `" "cos(A+B)=cosAcosB-sinAsinB`

Explanation:

`cos((pi/2)+x)=cos(pi/2)cosx-sin(pi/2)sinx`

`cos(pi/2)=0" "sin(pi/2)=1`

`cos((pi/2)+x)=cancel(cos(pi/2)cosx)^0-cancel(sin(pi/2))^1sinx`

`=-sinx`