trig equation lol?

Question

solve for x:
cos(2x) = 5sin^2x - cos^2x

been a long time since i did one of these... lol
plz. show each step

Answer 1

Use the identity:
cos2x = cos^2x - sin^2x
We get:
cos^2x - sin^2x = 5sin^2x - cos^2x
2cos^2x = 6sin^2x
sin^2x/cos^2x = 1/3
tan^2x = 1/3
tanx = +/- 1/√3
Since you have not specified a range of values we'll go with the range of the arctan or principal values:
-π/2 < x < π/2
So the answers are:
x = +/- π/6 [or +/- 30 degrees]