Answer to Question #256 in Trigonometry for Ron Burgundy

Question

Find all values of x for which 2sin(x) = sqrt(4+2sqrt3 cos(x))

Answer 1

2sin(x) = sqrt(4+2sqrt3 cos(x))
sin(x)>=0
4sin^2(x) = 4+2sqrt3 cos(x)
4-4cos^2(x) = 4+2sqrt3 cos(x)
-4cos^2(x) = 2sqrt3 cos(x)
cos(x)=0 or cos(x) = -sqrt(3) / 2
x = pi/2 + pi*n x = 5pi/6 + pi*n, nEZ
But sin(x)>=0 => x = pi/2 + 2pi*n x = 5pi/6 + 2pi*n, nEZ