csc^{2}(x/2)=2sec(x)

Please help me solve for x.

csc^{2}(x/2)=2sec(x)

Please help me solve for x.

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Take reciprocals,

sin^{2}(x/2) = cos(x)/2

=> 2sin^{2}(x/2) = cos(x)

=> 1-cos(x) = cos(x)

=> cos(x) = 1/2

=> x = pi/3, 5pi/3 on [0, 2pi).

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