SOLUTION: Gidday I have been asked to prove the following identity, and i have absolutely no idea what is being asked for. cos^2theta - sin^2theta = 1 - 2(sin^2theta) Thanks Dar

Algebra ->  Geometry-proofs -> SOLUTION: Gidday I have been asked to prove the following identity, and i have absolutely no idea what is being asked for. cos^2theta - sin^2theta = 1 - 2(sin^2theta) Thanks Dar      Log On


   

Question 28554: Gidday
I have been asked to prove the following identity, and i have absolutely no idea what is being asked for.
cos^2theta - sin^2theta = 1 - 2(sin^2theta)
Thanks Darryl
Found 2 solutions by longjonsilver, Paul:
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
cos%5E2%28A%29+-+sin%5E2%28A%29+

now, cos%5E2%28A%29+%2B+sin%5E2%28A%29+=+1+
so that cos%5E2%28A%29+=+1+-+sin%5E2%28A%29+

so, put that into the top equation, giving:
1+-+sin%5E2%28A%29+-+sin%5E2%28A%29+

which becomes 1+-+2sin%5E2%28A%29+ which is the other side of the Question... so this proves it.

jon.

Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
This trig indentiy is pretty complex to be thought of derivaties. SO in this indentiy solve by subsitution and develop your own identiy. FIrst we will find what sin^2x equals.

cos^2x-sin^2x=1-2(sin^2x)
cos^2x-sin^2x-1=-2(sin^2x)
-(cos^2x-sin^2x-1)/2=sin^2x
So a new trig identiy is formed. SUbsitute it into the original.

cos^2x-sin^2x = 1-2((-(cos^2x-sin^2x-1)/2) simplify
cos^2x-sin^2x = 1+cos^2x-sin^2x-1
cos^2x-sin^2x = cos^2x-sin^2x

Proven.
Paul.