maths

(sin x)^2 + (cos x)^2 = 1
Divide both side by (cos x)^2, then
(tan x)^2 + 1 = (sec x)^2= 1/ [(cos x)^2]

So sin x cos x [1 + (tan x)^2 ]
= sin x cos x { 1/ [(cos x)^2] }
= (sin x) / (cos x)
= tan x

左方=sinx cosx ( 1+ tan2x )
= sinx cosx (1/cos2x)
=sinx/cosx
=tanx
=右方
∴sinx cosx ( 1+ tan2x )= tanx是恒等式