Question

Given the identity sec(x)csc(x)(tan(x)+cot(x))=2+tan^2(x)+cot^2(x), prove the identity.

Answer 1

\[\sec (x) \csc (x)[\tan(x)+\cot(x)]=2+\tan^2 (x)+\cot^2 (x)\]

Answer 2

\[\sec x\csc x(\tan x+\cot x)=\frac{1}{\cos x\sin x}\left(\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x}\right)\]
Distribute the outer \(\dfrac{1}{\cos x\sin x}\) and see what happens

Answer 3

Might as well say it now...

You will be needing the following identities:
\[\csc^2x=1+\cot^2x\\
\sec^2x=1+\tan^2x\]