Trig identity

**Sakai** · May 31st 2010, 12:09 PM

Solve for $x\in R:$

$<br /> \sin^{3}{x}(1+\cot{x})+\cos^{3}{x}(1+\tan{x})=\cos {2x}<br />$

**sa-ri-ga-ma** · May 31st 2010, 05:16 PM

Originally Posted by Sakai

Solve for $x\in R:$

$<br /> \sin^{3}{x}(1+\cot{x})+\cos^{3}{x}(1+\tan{x})=\cos {2x}<br />$

$\sin^{3}{x}(1+\cot{x})+\cos^{3}{x}(1+\tan{x}) = \cos^{2}{x} - \sin^{2}{x}$

$\sin^{3}{x}+ \sin^{3}{x}\cot{x} + \cos^{3}{x} +\cos^{3}{x}\tan{x}= \cos^{2}{x} - \sin^{2}{x}$

$\sin^{3}{x} + \cos^{3}{x} + \sin^{3}{x}\frac{\cos{x}}{\sin{x}} + \cos^{3}{x}\frac{\sin{x}}{\cos{x}}= \cos^{2}{x} - \sin^{2}{x}$

Now factorize and simplify.

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