SOLUTION: Find the general solution of 2cos^2theta=1 I got two answers: 360n+-45 and 360n+- 135 Why is the first one the only answer?

Algebra ->  Trigonometry-basics -> SOLUTION: Find the general solution of 2cos^2theta=1 I got two answers: 360n+-45 and 360n+- 135 Why is the first one the only answer?       Log On


   

Question 1118105: Find the general solution of 2cos^2theta=1
I got two answers: 360n+-45 and 360n+- 135
Why is the first one the only answer?
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


The first one is NOT the only answer for the equation you show.

2cos%28x%29%5E2=1
cos%28x%29%5E2+=+1%2F2
cos%28x%29+=+sqrt%282%29%2F2 or cos%28x%29+=+-sqrt%282%29%2F2

Any angle with a reference angle of 45 degrees in ANY of the four quadrants satisfies the equation --
45+360n
135+360n
225+360n
315+360n

Or, stated more simply,
45+90n