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Math Help - Prove a trig identity

  1. #1
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    Prove a trig identity

    sin(x)+cos(x) = \frac{cos(x)}{1-tan(x)} +\frac{sin(x)}{1-cot(x)}
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  2. #2
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    Re: Prove a trig identity

    \displaystyle \begin{align*} \frac{\cos{x}}{1 - \tan{x}} + \frac{\sin{x}}{1 - \cot{x}} &\equiv \frac{\cos{x}}{1 - \frac{\sin{x}}{\cos{x}}} + \frac{\sin{x}}{1 - \frac{\cos{x}}{\sin{x}}} \\ &\equiv \frac{\cos{x}}{\frac{\cos{x} - \sin{x}}{\cos{x}}} + \frac{\sin{x}}{\frac{\sin{x} - \cos{x}}{\sin{x}}} \\ &\equiv \frac{\cos^2{x}}{\cos{x} - \sin{x}} + \frac{\sin^2{x}}{\sin{x} - \cos{x}} \\ &\equiv \frac{\cos^2{x}}{\cos{x} - \sin{x}} - \frac{\sin^2{x}}{\cos{x} - \sin{x}} \\ &\equiv \frac{\cos^2{x} - \sin^2{x}}{\cos{x} - \sin{x}} \\ &\equiv \frac{(\cos{x} - \sin{x})(\cos{x} + \sin{x})}{\cos{x} - \sin{x}} \\ &\equiv \cos{x} + \sin{x} \end{align*}
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  3. #3
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    Re: Prove a trig identity

    Thanks. I didn't see that, but it's simple.
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