# How do you prove cos(x)tan(X) + sin(x)cot(x) = sin(x) + cos^2(x)?

Jul 25, 2018

#### Explanation:

We know that,

$\diamond \tan \theta = \sin \frac{\theta}{\cos} \theta \mathmr{and} \cot \theta = \cos \frac{\theta}{\sin} \theta$

Given that

cosxtancolor(red)(x)+sinxcotx=sinx+color(red)(cos^2x

We take ,

$L H S = \cos x \tan x + \sin x \cot x$

$\textcolor{w h i t e}{L H S} = \cos x \left(\sin \frac{x}{\cos} x\right) + \sin x \left(\cos \frac{x}{\sin} x\right)$

$\textcolor{w h i t e}{L H S} = \sin x + \cos x \ne \sin x + {\cos}^{2} x$

So, $L H S \ne R H S$

Hence, we cannot prove the above result.