there are different ways of solving this:
one way is the follwing:
cos^2(x) -sin^2(x) =cos (2x)
then, equation becomes:
cos (2x) -sin (x)=0
but sin(x) is also equivalent to : cos ((pi/2)-x),
so, the equation now is:
cos (2x) - cos ((pi/2)-x)=0 -------> cos (2x) = cos ((pi/2)-x) ---------> 2x=(pi/2) -x
but since it is an angle, the answer would be repeating so:
2x= 2k(pi) +((pi/2)-x)
3x= pi( 2k+1/2)
x= (pi/3) (2k+1/2)
for k=0, x= pi/6
for k=1, x= 5pi/6
for k=2, x= 3pi/2
