The numbers of integral of 'a' for which the equation is satisfied
$4 sin (X + 3 \frac{π}{3}) cos (X - 3 \frac{π}{6}) = a^{2} + \sqrt{3} sin 2 X - cos 2 X$

2

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3

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4

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5

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Solution

The correct option is D $5$
$2 (sin (2 x + \frac{π}{6}) + sin \frac{π}{2}) = a^{2} + \sqrt{3} sin 2 x - cos 2 x$
$2 (sin 2 x \cdot \frac{\sqrt{3}}{2} + cos 2 x \cdot \frac{1}{2} + 1) = a^{2} + \sqrt{3} sin 2 x - cos 2 x$
2cos 2x +2 = $a^{2}$ - cos 2x
2cos 2x = $a^{2}$ - 2
$- 2 \leq a^{2} - 2 \leq 2$
$O \leq a^{2} \leq 4 \Rightarrow a ϵ [- 2, 2]$

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