Question

Помогите, пожалуйста, решить уравнения.

Answer 1

$1),, sin x-16sin^5x=0\ sin x(1-16sin^4x)=0\sin x=0\ x= pi k,k in Z\ sin^4x= frac{1}{16} \ sin^4x= frac{1}{2^4} \ \ sin x=pm frac{1}{2} \ x=(-1)^kcdot frac{pi}{6} + pi k,k in Z\ x=(-1)^{k+1}cdot frac{pi}{6} + pi k,k in Z$

$8cos^4x+cos x=0\ cos x(8cos^3 x+1)=0\ cos x=0\ x= frac{pi}{2}+ pi n,n in Z\ \ cos x=-0.5\ x=pm frac{2 pi }{3} +2 pi n,n in Z$

Второе задание
$sin^3x+3sin^2xcos x-sin xcos^2x-3cos^3x=0\ sin x(sin^2x-cos^2x)+3cos x(sin^2x-cos^2x)=0\ -sin xcos 2x-3cos xcos2x=0\ -cos2x(sin x+3cos x)=0\ cos2x=0\ x= frac{pi}{4}+ frac{pi n}{2},n in Z\ \ sin x+3cos x=0|:cos x\ tgx+3=0\ x=-arctg3+ pi n,n in Z$

$6cos^3x+3cos^2xsin x-2cos xsin^2x-sin^3x=0\ 3cos^2x(2cos x+sin x)-sin^2x(2cos x+sin x)=0\ (2cos x+sin x)(3cos^2x-sin^2x)=0\ 2cos x+sin x=0|:cos x\ 2+tgx=0\ x=-arctg2+ pi n,n in Z\ \ 3cos^2x-sin^2x=0|:cos ^2x\ 3-tg^2x=0\ tg x=pm sqrt{3}\ x=pm frac{pi}{3}+ pi n,n in Z$

Answer 2

спасибо большое