8sin(x) = ((√3)/(cos(x))) + (1/(sin(x))) ⇒ x=?


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Question Number 147640 by mathdanisur last updated on 22/Jul/21

$8 s i n (x) = \frac{\sqrt{3}}{c o s (x)} + \frac{1}{s i n (x)} \Rightarrow x = ?$
	Answered by gsk2684 last updated on 25/Jul/21

	$8 \sin^{2} x \cos x = \sqrt{3} \sin x + \cos x$ $4 \sin 2 x \sin x = \sqrt{3} \sin x + \cos x$ $2 (2 \sin 2 x \sin x) = \sqrt{3} \sin x + \cos x$ $2 (\cos x - \cos 3 x) = \sqrt{3} \sin x + \cos x$ $\cos x - \sqrt{3} \sin x = 2 \cos 3 x$ $\frac{1}{2} \cos x - \frac{\sqrt{3}}{2} \sin x = \cos 3 x$ $\cos (\frac{π}{3} + x) = \cos 3 x$ $\frac{π}{3} + x = 2 k π \pm 3 x w h e r e k \in Z$ $\frac{π}{3} + x = 2 k π + 3 x o r \frac{π}{3} + x = 2 k π - 3 x$ $- 2 x = 2 k π - \frac{π}{3} o r 4 x = 2 k π - \frac{π}{3}$ $x = - k π + \frac{π}{6} o r \frac{k π}{2} - \frac{π}{12}, k \in Z$ $x = k π + \frac{π}{6} o r \frac{k π}{2} - \frac{π}{12}, k \in Z$
	Commented by mathdanisur last updated on 22/Jul/21

	$T h a n k y o u S i r$
	Commented by mathdanisur last updated on 25/Jul/21

	$t h a n k y o u S i r$
	Commented by mathdanisur last updated on 23/Jul/21

	$a n s w e r \frac{π}{6} + π k$
	Commented by gsk2684 last updated on 25/Jul/21

	$i w r o t e g e n e r a l s o l u t i o n n o w$
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