Question

sinx+cos4x*sinx=0
помогите

Answer 1

$\sin\left(x\right)\,\cos\left(4\,x\right)+\sin\left(x\right)=0\Leftrightarrow \sin\left(x\right)\,\left(\cos\left(4\,x\right)+1\right)=0\\\sin(x)=0\Rightarrow x=\pi\,\mathrm{k}, \mathrm{k}\in \mathbb{Z}\\\cos\left(4\,x\right)+1=0\Leftrightarrow \cos\left(4\,x\right)=-1\Rightarrow 4\,x=2\,\pi\,\mathrm{k}+\pi\Rightarrow x=\dfrac{\pi\,\mathrm{k}}{2}+\dfrac{\pi}{4}, \mathrm{k}\in \mathbb{Z}$