I need some hints on proving an identity

A Beautiful Mind · #1 $Old$ October 31st, 2009, 05:54 PM

$sin^4x + 2sin^2x cos^2x + cos^4x = 1$

Alright. I wouldn't like to know the solution, but I would like some help in solving this.

It looks to me like I need to do a lot of simplifying. A thing I do know:

$sin^2x+cos^2x=1$

I'm not sure, but I think if you rearranged the terms you could get $sin^4x+cos^4x+2sin^2xcos^2x$ and then maybe break up the $sin^4x+cos^4x$ into $(sin^2x)(sin^2x)+(cos^2x)(cos^2x)$ . Maybe do that for the other term as well? $(sinx)(sinx)(cosx)(cosx).$

Defunkt · #2 $Old$ October 31st, 2009, 06:12 PM

Quote:

Originally Posted by A Beautiful Mind $View Post$

$sin^4x + 2sin^2x cos^2x + cos^4x = 1$

Alright. I wouldn't like to know the solution, but I would like some help in solving this.

It looks to me like I need to do a lot of simplifying. A thing I do know:

$sin^2x+cos^2x=1$

I'm not sure, but I think if you rearranged the terms you could get $sin^4x+cos^4x+2sin^2xcos^2x$ and then maybe break up the $sin^4x+cos^4x$ into $(sin^2x)(sin^2x)+(cos^2x)(cos^2x)$ . Maybe do that for the other term as well? $(sinx)(sinx)(cosx)(cosx).$

$(sin^2(x) + cos^2(x))^2 = ?$