Question

How do you simplify `cos^2 5x- sin^2 5x`?

Answer 1

`f(x) = cos^2 5x - sin^2 5x = (cos 5x - sin 5x)(cos 5x + sin 5x)`
We can go further:
`(cos 5x - sin 5x) = sqrt2.sin(45 - 5x)`
`(cos 5x + sin 5x) = sqrt2.sin(45 + 5x)`

Finally,`f(x) = 2.sin (45 - x).sin (45 + x)`