Verifying this Trigonometric Identity

[Ivan92]

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 can't 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 can't seem to simplify the other side. Any assistance is awesome.

 

[stevenb]

Start by factoring a sin^2 (a) from the sum on the right hand side. Then represent 2 as 1+1.

I think you'll see the rest after that.

 

[Ivan92]

Ahh Awesome! Thank you StevenB. I appreciate it. My younger brother says thanks too. Haha! :)