SOLUTION: How can I prove this identity? (1-cos^2theta)(1+cos^2theta)=2sin^2theta-sin^4theta? I tried to do it, and this is what I've come up with so far, and am not sure if I am doing it

Algebra ->  Trigonometry-basics -> SOLUTION: How can I prove this identity? (1-cos^2theta)(1+cos^2theta)=2sin^2theta-sin^4theta? I tried to do it, and this is what I've come up with so far, and am not sure if I am doing it      Log On


   

Question 591078: How can I prove this identity? (1-cos^2theta)(1+cos^2theta)=2sin^2theta-sin^4theta?
I tried to do it, and this is what I've come up with so far, and am not sure if I am doing it correctly.
Working with the left side, I have the following:
sin^2theta(1+cos^2theta) =
sin^2theta+(sin^2theta*cos^2theta)
And then it stops.
Found 2 solutions by Alan3354, scott8148:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
How can I prove this identity? (1-cos^2theta)(1+cos^2theta)=2sin^2theta-sin^4theta?
I tried to do it, and this is what I've come up with so far, and am not sure if I am doing it correctly.
Working with the left side, I have the following:
sin^2theta(1+cos^2theta) =
sin^2theta+(sin^2theta*cos^2theta)
---------------
(1-cos^2theta)(1+cos^2theta)=2sin^2theta-sin^4theta?
sin^2(t)*(1+cos^2theta)=2sin^2theta - sin^4theta?
(1+cos^2theta) = 2 - sin^2theta?
1+cos^2theta + sin^(t) = 2
cos^2(t) + sin^(t) = 1
I'm convinced.

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
FOILing the left side ___ 1 - cos^4 = 2 sin^2 - sin^4

adding (sin^4 - 1) ___ sin^4 - cos^4 = 2 sin^2 - 1

factoring ___ (sin^2 + cos^2) (sin^2 - cos^2) = 2 sin^2 - (sin^2 + cos^2)

1 (sin^2 - cos^2) = sin^2 - cos^2

1 = 1