Question

How do you simplify using the double angle formula `cos^2(-105)-sin^2(-105)`?

Answer 1

`-sqrt 3/2.`

Explanation:

Recall that

`(1) : cos 2theta=cos^2 theta-sin^2 theta.`

`(2) : cos (-theta)=cos theta, &, (3) : cos (180+theta)=-cos theta.`

Here, `theta = -105", so the expression = "cos(2*(-105))`

`=cos (-210)=cos (210) =cos (180+30)=-cos 30=-sqrt 3/2.`