# How do you verify sinx + cosx cotx = cscx?

Apr 16, 2015

Left Hand Side :

$\sin x + \cos x \cot x$

We know that color(blue)(cot x = cos x / sin x

Therefore $\sin x + \cos x \cot x = \sin x + \cos x \cdot \left(\cos \frac{x}{\sin} x\right)$

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

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

(We know the Trigonometric Identity
color(blue)( sin^2x + cos ^ 2 x = 1)

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

$= \csc x$ (Because Cosecant is the reciprocal of Sine)

Hence Proved.