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Math Help - Trigonomic Identities Help?

  1. #1
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    Trigonomic Identities Help?

    I have trouble proving this. Thanks for any help in advanced!

    Prove the following:

    tanxsinx tanx - sinx
    tanx + sinx = tanxsinx
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    \frac{\tan (x)\sin (x)}{\tan (x)+\sin (x)}=\frac{\tan (x)\sin (x)\left( \tan (x)-\sin (x) \right)}{\tan ^{2}(x)\sin ^{2}(x)}=\frac{\tan (x)-\sin (x)}{\tan (x)\sin (x)}.

    Observe that \tan ^{2}(x)-\sin ^{2}(x)=\sin ^{2}(x)\left( \frac{1}{\cos ^{2}(x)}-1 \right)=\tan ^{2}(x)\sin ^{2}(x), and we're done. \blacksquare
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