SOLUTION: prove (we have to work with the left side) cos(2u)=cos^2u

Algebra ->  Trigonometry-basics -> SOLUTION: prove (we have to work with the left side) cos(2u)=cos^2u      Log On


   

Question 155226This question is from textbook precalculus
: prove (we have to work with the left side)
cos(2u)=cos^2u This question is from textbook precalculus

Found 2 solutions by stanbon, jojo14344:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Are you sure you are being asked to prove this
is an identity. It is not an identity.
Possible you are being asked to solve this
equation. That can be done.
------------------
Cheers,
Stan H.

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
cos%282u%29=cos%5E2%28u%29
By double -Angle Formula:
cos%282u%29=2cos%5E2%28u%29-1
So,
2cos%5E2%28u%29-1=cos%5E2%28u%29
2cos%5E2%28u%29-cos%5E2%28u%29=1
cos%5E2%28u%29%282-1%29=1
cos%5E2%28u%29=1
cos%5E2%28u%29-1=0
By Pythagorean Identities:
sin%5E2%28u%29%2Bcos%5E2%28u%29=1
sin%5E2%28u%29=1-cos%5E2%28u%29
Therefore,
cos%5E2%28u%29-1 -----------> -sin%5E2%28u%29
Thank you,
Jojo