# Verifying this Trigonometric Identity

Hey guys. How are you all doing? I'm helping my younger brother out with his trigonometry homework. He is dealing with verifying trigonometric identities. However, he has the problem that I am getting nowhere with. Hope you all can help. Thanks in advance. :)

## Homework Statement

Verify (1-cos^2 (a))(1+cos^2(a)) = 2sin^2 (a) -sin^4 (a). I cant simplify the (1+cos^2(a)). Also can not tell if I can simplify the other side as well.

## Homework Equations

sin^2 a + cos^2 a = 1

## The Attempt at a Solution

So using the Pythagorean identity, I have been able to simplify this to:

(sin^2 (a))(1+cos^2) ) = 2sin^2 (a) -sin^4 (a).

I am just stuck in simplifying the part after sin^2 (a). Also cant seem to simplify the other side. Any assistance is awesome.