SOLUTION: Prove sin^2 x cos^2 x + cos^4 x = (1-sinx) (1+sinx) is an identity. I need steps please

Algebra ->  Rational-functions -> SOLUTION: Prove sin^2 x cos^2 x + cos^4 x = (1-sinx) (1+sinx) is an identity. I need steps please      Log On


   

Question 1159430: Prove sin^2 x cos^2 x + cos^4 x = (1-sinx) (1+sinx) is an identity. I need steps please
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
sin^2 x cos^2 x + cos^4 x = (1-sinx) (1+sinx)=(1-sin^2x)=cos^2x
left side factor out a cos^2x and get cos^2x(sin^2x+cos^2x)
but sin^2x+cos^2x=1
so cos^2 x (1)=cos^2 x
the key identities are cos^2x+sin^2 x=1
and 1-sin^2x=cos^2 x
and 1-cos^2 x= sin^2 x