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The solution set of equation 4 sin theta cos theta -2cos theta -2root3 sin theta + root3 =0 in the interval of( 0, pi) is

The solution set of equation 4 sin theta cos theta -2cos theta -2root3 sin theta + root3 =0 in the interval of( 0, pi) is

Question Image
Grade:11

1 Answers

Faiz
107 Points
4 years ago
The expression can be rearranged as:4sinx cosx - 2√3sinx - 2cosx + √3 = 02sinx ( 2cosx - √3 ) - 1 ( 2cosx - √3 ) = 0( 2sinx - 1 ) ( 2cosx - √3 ) = 0Either sin x = 1/2 or cos x = √3/2 or both can be satisfied.sin x = 1/2 gives x = π/6, 5π/6 and cos x = √3/2 gives x = π/6, 11π/6 in the interval (0,2π)Combining both x = π/6, 5π/6, 11π/6So according to your attached image answer is option D.

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