Question

3sin^2x-7,5cos2x-1,5=0
Пожалуйста помогите

Answer 1

$3sin^2x-7,5cos2x-1,5=0\\3sin^2x-7,5(1-2sin^2x)-1,5=0\\3sin^2x-7,5+15sin^2x-1,5=0\\18sin^2x-9=0\\18sin^2x=9\\sin^2x=\frac{1}{2}\\\boxed{sinx=\pm \frac{\sqrt2}{2}}\\sinx= \frac{\sqrt2}{2}\,\,\,\,our\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,sinx=- \frac{\sqrt2}{2}\\x=(-1)^k\, \frac{\pi}{4}+\pi k,k\in\mathbb{Z} \,\,\,\,\,\,x=(-1)^{k+1}\, \frac{\pi}{4}+\pi k, k\in \mathbb{Z}$