Ask Me Help Desk - Prove that trig identity

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prove that trig identity

(csc(x) cot(x))(1-cos(x))=sin(x)

Use $\sin x=\cos x\tan x$ and $\sin^2 x+\cos^2 x=1$ :

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

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