Ask Me Help Desk - Prove this trig identity please

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prove this trig identity please

sec(x) csc(x)/1 tan(x)=csc(x)

********that is 1+tan(x) on the bottom my typo********

Use $\sin x=\cos x\tan x$ :

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

Oh, a typo at the last equal sign: it is obviously $\frac{1}{\sin x}$ .

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