Question

Prove that `cos(pi-theta)=-costheta` using the compound angle formulae?

Answer 1

See below

Explanation:

There is a rule for the expansion of compound angles for sine, cosine and tangent functions. For the sake of this answer, I'll only go over the cosine compound angle formulae.

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

`thereforecos(vartheta-pi)=cosvarthetacospi-sinvarthetasinpi=-cosvartheta`

Proof for the compound angle formulae can be found here.