SOLUTION: how do you solve 3cos^2x=2sin^2x+2

Algebra ->  Trigonometry-basics -> SOLUTION: how do you solve 3cos^2x=2sin^2x+2       Log On


   

Question 1149982: how do you solve 3cos^2x=2sin^2x+2
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Replace cos^2x with 1-sin^2x to obtain a quadratic equation in sinx; or replace sin^2x with 1-cos^2x to obtain a quadratic equation in cosx.

Then solve the quadratic in sinx or cosx exactly the same way you would solve a quadratic in x.

3%28cosx%29%5E2+=+2%28sinx%29%5E2%2B2
3%28cosx%29%5E2+=+2%281-%28cosx%29%5E2%29%2B2
3%28cosx%29%5E2+=+2-2%2Acos%28x%29%5E2%2B2+=+4-2%2Acos%28x%29%5E2
5%28cos%28x%29%5E2%29+=+4
cos%28x%29%5E2+=+4%2F5

...