SOLUTION: Can you please solve this equation and find all solutions? And give an explanation? I am not sure whether to write it like this: {{{ 4cos(2x)^2 - 1 = 0 }}} or like this:

Algebra ->  Trigonometry-basics -> SOLUTION: Can you please solve this equation and find all solutions? And give an explanation? I am not sure whether to write it like this: {{{ 4cos(2x)^2 - 1 = 0 }}} or like this:       Log On


   

Question 437816: Can you please solve this equation and find all solutions? And give an explanation?
I am not sure whether to write it like this:
+4cos%282x%29%5E2+-+1+=+0+
or like this:
4cos^2(2x) - 1 = 0
Thank you
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The 2 ways to write it shown make it 2 different problems.
If it's cosine squared, it's
4cos^2(2x) - 1 = 0
-------------------------
cos^2(2x) = 1/4
cos(2x) = ± 1/2
------------
cos(2x) = +1/2
2x = 60 degs + n*360, n = 0,1,2,3...
x = 30 degs + n*180, n = 0,1,2,3...
2x = 300 degs + n*360, n = 0,1,2,3...
x = 150 degs + n*180, n = 0,1,2,3...
---------------
cos(2x) = -1/2
2x = 120 degs + n*360, n = 0,1,2,3...
x = 60 + n*180, n = 0,1,2,3...
-------
2x = 240 degs + n*360, n = 0,1,2,3...
x = 120 + n*180, n = 0,1,2,3...