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Math Help - one more identity to prove

  1. #1
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    Post one more identity to prove

    Thanks for having a look.

    <br />
\frac{sin2x}{cosx}+\frac{cos2x}{sinx}=cscx<br />
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  2. #2
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    Quote Originally Posted by nightrider456 View Post
    Thanks for having a look.

    <br />
\frac{sin2x}{cosx}+\frac{cos2x}{sinx}=cscx<br />
    \frac{\sin{2x}}{\cos{x}} + \frac{\cos{2x}}{\sin{x}} = \frac{2\sin{x}\cos{x}}{\cos{x}} + \frac{\cos^2{x} - \sin^2{x}}{\sin{x}}

     = 2\sin{x} + \frac{\cos^2{x} - \sin^2{x}}{\sin{x}}

     = \frac{2\sin^2{x} + \cos^2{x} - \sin^2{x}}{\sin{x}}

     = \frac{\sin^2{x} + \cos^2{x}}{\sin{x}}

     = \frac{1}{\sin{x}}

     = \csc{x}.
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  3. #3
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    \frac{\sin 2x}{\cos x}+\frac{\cos 2x}{\sin x}=\frac{\cos (2x-x)}{\sin (x)\cos (x)}=\csc x.
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