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JEE MATHEMATICS MCQ: PROPERTIES OF TRIANGLES

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In a Δ  ABC\Delta \;ABC, angle AA is greater than angle BB. If the measures of angles AA and BB satisfy the equation 3sin⁡x−4sin⁡3x−k=0,    0<k<13\sin x - 4{\sin ^3}x - k = 0,\;\;0 < k < 1, then the measure of angle CC is
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Correct option: C
2π3\frac{{2\pi }}{3}
Option C (2π3\frac{{2\pi }}{3}) is correct because the given equation implies sin⁡3A=sin⁡3B\sin 3A = \sin 3B, and since A > B, we have A+B=60∘A + B = 60^\circ, leading to C=120∘=2π3C = 120^\circ = \frac{{2\pi }}{3}.

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