Question

Suppose f(x)=cos x - sin x and g(x)=cos x + sin x. Explain why the graph of (fxg)(x) is equivalent to the graph of h(x)=cos x after it has been horizontally compressed by a factor of 1/2. Please help, thank you!

Answer 1

(fxg)(x) = (cosx - sinx)(cosx + sinx)
= cos^2 x - sin^2 x
= cos 2x , by definition.

notice the period of the new one is 2π/2 = π
while the period of the first one was 2π
notice the compression by a factor of 1/2 ?

Answer 2

Oh your right! Now I see that, thanks so much!