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trig function

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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 -

    (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 -

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

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