SOLUTION: Ive been trying to work this out for a while now and can't get it, please help! Prove: cos2x+2sin^2x=1 Thanks!

Algebra ->  Trigonometry-basics -> SOLUTION: Ive been trying to work this out for a while now and can't get it, please help! Prove: cos2x+2sin^2x=1 Thanks!       Log On


   

Question 811471: Ive been trying to work this out for a while now and can't get it, please help!
Prove:
cos2x+2sin^2x=1
Thanks!

Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
Using the trig identity cos(2x) = 2cos^2(x) - 1 we can write the LHS of the equation as
2cos^2(x) - 1 + 2sin^2(x) -> 2(cos^2(x) + sin^2(x)) - 1
Since sin^2(x) + cos^2(x) = 1, the LHS becomes 2 - 1 = 1