Please help me to solve it in [−π;0] cos2x+cosx+1=sin3x+sin2x+sinx Explain details if possible.


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Question Number 77027 by mathocean1 last updated on 02/Jan/20

$Please help me to solve it in [- π; 0]$ $\cos 2 x + \cos x + 1 = \sin 3 x + \sin 2 x + \sin x$ $E xplain details if possible .$
	Answered by mr W last updated on 02/Jan/20

	$\cos 2 x + \cos x + 1 = \sin 3 x + \sin 2 x + \sin x$ $2 \cos^{2} x + \cos x = 3 \sin x - 4 \sin^{3} x + 2 \sin x \cos x + \sin x$ $(2 \cos x + 1) \cos x = 2 \sin x \cos x (2 \cos x + 1)$ $(2 \cos x + 1) (2 \sin x - 1) \cos x = 0$ $\Rightarrow \cos x = 0 \Rightarrow x = - \frac{π}{2}$ $\Rightarrow \cos x = - \frac{1}{2} \Rightarrow x = - \frac{2 π}{3}$ $\Rightarrow \sin x = \frac{1}{2} \Rightarrow n o s o l u t i o n w i t h i n [- π, 0]$ $\Rightarrow s o l u t i o n s a r e : x = - \frac{2 π}{3}, - \frac{π}{2}$
	Commented by mathocean1 last updated on 02/Jan/20

	$thank you sir$
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