Question

A cos^2 ax - a sin^2 ax=?

Answer 1

By the cosine double angle formula,

`a cos ^2(ax) - a sin ^2(ax) = a cos(2ax)`

Explanation:

Recall the cosine sum angle formula,

`cos(A+B) = cos A cos B - sin A sin B`

When `A=B` we get the first form of the cosine double angle formula:

`cos(2A)= cos^2 A - sin ^2 A`

which matches the problem nicely.

`a cos ^2(ax) - a sin ^2(ax)`

`= a(cos^2(ax) - sin ^2 (ax)`

`= a cos(2ax)`