Question

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

Answer 1

$(\tan x+1)^2=\tan^2x+2\tan x+1$
$=\sec^2x+2\tan x$
$=\dfrac1{\cos^2x}+2\dfrac{\sin x}{\cos x}$
$=\dfrac1{\cos^2x}+\dfrac{2\sin x\cos x}{\cos^2x}$
$=\dfrac{1+2\sin x\cos x}{\cos^2x}$