Question

Prove the identity. (tanx+1)^2=(1+2sinxcosx)/(cos^2x)

Answer 1

`(\tan x+1)^2=\tan^2x+2\tan x+1`

`=\sec^2x+2\tan x`

`=\frac1{\cos^2x}+2(\sin x)/(\cos x)`

`=\frac1{\cos^2x}+(2\sin x\cos x)/(\cos^2x)`

`=(1+2\sin x\cos x)/(\cos^2x)`