Thread: Solve trig equation

could anyone please show how to solve this step by step.
All help is appreciated!

solve the equation for 0< x< 2 pi .

sin^2 X = 3 cos^2 X


thanks!!

I'd make a substitution and see what dropped out.

sin ^2 x - 3cos^2 x = 0
1-cos ^2 x - 3cos ^2x= 0
4 cos ^2 x -1 = 0
cos ^2 x = 1/4
cos x = 1/2

using special angles you find that its 60 and 300 degrees.