Question

How do you verify the identity `cos(180+x)=-cosx`?

Answer 1

Use the sum in cosine identity,

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

Thus we have:

`cos(180˚)cos(x) - sin(180˚)sinx = -cosx`

`-1(cosx) - 0(sinx)= -cosx`

`-cosx= -cosx`

`LHS = RHS`

As required.

Hopefully this helps!