, the solution set of equation 4sin theta into cos theta - 2 cos theta minus 2 root 3 sin theta + root 3 is equal to zero in the interval 0 to 2 pie is

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i have taken variable as x instead of theta (0 is zero) 4sinx cosx - 2cosx -2√3sinx + √3 =0 The expression can be rearranged as 4sinx cosx - 2√3sinx - 2cosx + √3=0 2sinx ( 2cosx - √3 ) - 1 ( 2cosx - √3 )=0 ( 2sinx - 1 ) ( 2cosx - √3 ) =0 Either ( 2sinx - 1 )=0;0r ( 2cosx - √3 ) =0 sin x = 1/2 or cos x = √3/2 or both can be satisfied. sin x = 1/2 gives x = π/6, 5π/6 in the interval (0,2π) and cos x = √3/2 gives x = π/6, 11π/6 in the interval (0,2π) Combining both x = π/6, 5π/6, 11π/6 in the interval (0,2π)

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