Posted by **Kjd** on Thursday, May 17, 2012 at 7:10pm.

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!

- trig function -
**Reiny**, Thursday, May 17, 2012 at 7:46pm
(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 ?

- trig function -
**Kjd**, Thursday, May 17, 2012 at 7:56pm
Oh your right! Now I see that, thanks so much!

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