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Hello, thank you for taking the time to answer my question. It is solving the multiple-angle equation:

cos(x/2) = -(sqrt3)/2

The basic angle of this equation is given by arcos(sqrt3)/2 = pi/6;

since the cosine function is negative in the 2nd and 3rd quadrant,

we have x/2 = pi- pi/6 or pi + pi/6

x/2 = 5pi/6, 7pi/6

Hence x= 5pi/3, 7pi/3 (shown)

Depending on the range of values of x (which in this case was not specified), you may have a greater or lesser quantity of answers.

Hope this helps. Peace.

Calculus

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