Question

Verify cos(180+x)=-cosx
Please note the 180 is in degrees.

Answer 1

The angle sum identity for cosine says that


`\cos(180^\circ+x)=\cos180^\circ\cos x-\sin180^\circ\sin x=-\cos x`

because
`\cos180^\circ=-1` and
`\sin180^\circ=0`.