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In a D ABC, angle A is greater than angle B. If the measures of angles A and B satisfy the equation $3 Sin x - 4 \sin^{3} x - k = 0, 0 < k < 1,$ then the measure of angle ‘C’ is

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$2 π / 3$

$π / 3$

$5 π / 6$

$π / 2$

answer is C.

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Detailed Solution

$3 \sin x - 4 \sin^{3} x = k k = \sin 3 x A, B satisfies the eqn . \sin 3 A = \sin 3 B 3 A = π - 3 B 3 a + 3 B = π A + B = \frac{π}{3} C = \frac{2 π}{3}$

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