Question 608023
cos^2 2x + 3sin2x = 3
First, we can use the identity cos^2(2x) = 1 - sin^2(2x) to obtain a quadratic in sin(2x):
1 - sin^2(2x) + 3sin(2x) - 3 = 0
sin^2(2x) - 3sin(2x) + 2 = 0
This can be factored as:
(sin(2x) - 1)(sin(2x) - 2) = 0
The LHS will be equal to 0 if either sin(2x) = 1, or sin(2x) = 2
Since the sine of any angle can never be >1, the only solutions are obtained for sin(2x) = 1 
In the 1st quadrant, this gives 2x = 90 deg -> x = 45 deg [{{{pi}}}/4]