Question

Verify the identity:
cos(x+π/2)= -sinx

Answer 1

This result can be verified using a trigonometric identity.

Explanation:

We use the the trigonometric identity

`cos(a\:{\pm}\:b)=cos(a)*cos(b){\mp}sin(a)*sin(b).`

In our case
`a=x` and
`b=\pi /2`, thus:

`cos(x+(\pi)/(2) )=cos(x)*cos((\pi)/(2))-sin(x)*sin((\pi)/(2)).`

Since

`cos((\pi)/(2))=0` and

`sin((\pi)/(2))=1`

the above equation simplifies as

`cos(x+(\pi)/(2) )=cos(x)*cos((\pi)/(2))-sin(x)*sin((\pi)/(2))=-sin(x)`

`\boxed{cos(x+(\pi)/(2) )=-sin(x)}`

thus proving the identity.