Question

3sin2x+sinxcosx-2cos2x = 0

Answer 1

Дополнительные формулы:
$\sin 2x=2\sin x\cos x$
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$3\sin 2x+\sin x\cos x-2\cos 2x=0$
$3\sin 2x+ \frac{2\sin x\cos x}{2} -2\cos 2x=0 \\ 3\sin 2x+ \frac{\sin 2x}{2} -2\cos2x=0|\cdot 2 \\ 6\sin 2x+\sin 2x-4\cos 2x=0 \\ 7\sin 2x-4\cos 2x=0|:\cos 2x \\ 7tg2x-4=0 \\ tg2x= \frac{4}{7} \\ 2x=arctg\frac{4}{7}+ \pi n,n \in Z \\ x= \frac{arctg\frac{4}{7}+\pi n}{2} , n \in Z$