Use substitution: sinx = sqrt(1-cos^2)
[tex]2- cos x = \sqrt{3} \sqrt{1-cos^2 x} \\ \\ (2-cos x)^2 = 3(1-cos^2 x)[/tex]
At this point, use another substitution, u = cos x
Then solve the quadratic for u
[tex](2-u)^2 = 3(1-u^2) \\ \\ 4u^2 -4u+1 = 0 \\ \\ u = \frac{1}{2} [/tex]
Sub back in cos x
[tex] cos x = \frac{1}{2} \\ \\ x = \frac{\pi}{3} [/tex]
