Prove that (tanx)^2-(sinx)^2=(tanx)^2(sinx)^2

We need to prove that: (tan x)^2 - (sin x)^2 = (tan x)^2
*(sin x)^2

Let's start from the left hand
side:

(tan x)^2 - (sin
x)^2

tan x = sin x / cos
x

=> (sin x)^2 / (cos x)^2 - (sin
x)^2

=> (sin x)^2 / (cos x)^2 - (sin x)^2 * (cos
x)^2 / (cos x)^2

=> [(sin x)^2 - (sin x)^2 * (cos
x)^2] / (cos x)^2

=> [(sin x)^2 * ( 1 - (cos x)^2)]
/ (cos x)^2

=> [(sin x)^2 * (sin x)^2] / (cos
x)^2

=> [(sin x)^2 / (cos x)^2] * (sin
x)^2]

=> (tan x)^2 * (sin
x)^2

This is the right hand
side.

This proves that (tan x)^2 - (sin x)^2
= (tan x)^2 *(sin x)^2