# Answer to Question #256 in Trigonometry for Ron Burgundy

Question #256

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

Expert's answer

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

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

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