Question

Помогите решить уравнения

Answer 1

$4\cos^2x-4\sin x+1=0\Leftrightarrow 4\,\left(1-\sin^{2}\left(x\right)\right)-4\,\sin\left(x\right)+1=0\\\sin x=t, \; |t|\leq 1\Rightarrow 4\,t^{2}+4\,t-5=0\Rightarrow t_{1,2}=\dfrac{{-2\pm \sqrt{24}}}{4}\Rightarrow x=\left(-1\right)^{\mathrm{k}}\,\arcsin\left(\frac{\sqrt{6}-1}{2}\right)+\pi\,\mathrm{k}$$2\cos^2x+5\sin x+1=0\Leftrightarrow 2\,\left(1-\sin^{2}\left(x\right)\right)+5\,\sin\left(x\right)+1=0\\\sin x=t, \; |t|\leq 1\Rightarrow 2\,t^{2}-5\,t-3=0\Rightarrow t=\left \{ -\frac{1}{2},3 \right \}\Rightarrow x=(-1)^{k+1}\frac{\pi}{6}+\pi k,k\in \mathbb{Z}$