Question

Verify the identity

cos quantity x plus pi divided by two = -sin x

Answer 1

Identity is verified.

Explanation:

We have to verify the identity
`cos(x+(\pi )/(2)) = (- sinx)`

To prove any identity we always prove one side(either left hand side or right hand side) of the equation equal to the other side.

In this identity we take the left hand side first

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

`=cosx* cos(\pi/2)-sinx* sin(\pi/2))` (as we know cos(a+b) = cosa×cosb-sina×sinb)

`= cosx*0-sinx*1`

`= 0-sinx`

= - sinx ( Right hand side)

Hence identity is proved.