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Math Help - help!

  1. #1
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    help!

    If cos Θ + sin Θ = √2 cos Θ;
    show that cos Θ - sin Θ = √2 sin Θ.
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  2. #2
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    Quote Originally Posted by snigdha View Post
    If cos Θ + sin Θ = √2 cos Θ;
    show that cos Θ - sin Θ = √2 sin Θ.
    Divide the first of those equations by \cos\theta to see that \tan\theta = \sqrt2-1. Similarly, the second equation is equivalent to \tan\theta = \frac1{\sqrt2+1}. Now complete the argument by showing that \sqrt2-1 = \frac1{\sqrt2+1},
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