Question

8sin^2 x-7=3sin 2x
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Answer 1

$8sin^2x-7=3sin 2x\\8sin^2x-7sin^2x-7cos^2x-6sinxcosx=0\\sin^2x-6sinxcosx-7cos^2x=0|:cos^2x\\tg^2x-6tgx-7=0\\tgx_{1,2}=3^+_-4\\tgx_1=7\ \ \ \ \ \ \ \ \ \ \ \ \ \ tgx_2=-1\\x_1=arctg7^+_-\pi n;\ \ x_2=-\frac{\pi}{4}^+_-\pi n;n\in Z$