solve:
3sin^2x-cos^2x=0

4sin^2x-3=0

3sin^2x-cos^2x

= 3 (1 - cos^2x) -cos^2x
= 3 - 4 cos^2x

Hence 4 cos^2x = 3

cos^2 x = 3/4

cos x = (+ or -) sqrt (3)/2

Remember: cos 30 = sqrt (3)/2

And cos (180 - 30) = - cos 30

From above: x = 30, 150,.


In the second case:

sin^2x = 3/4

On same principles, sin^2 60 = 3/4, sin^2 (180 +60) = 3/4

x = 60, 240,.