Question

1)2cos(П/3-3x)-корень3=0

2)3+4sin(2x+1)=0

Answer 1

$1)~ 2cos ( frac{pi}{3} -3x)-sqrt{3}=0\ \ cos (frac{pi}{3} -3x)= frac{sqrt3}{2}\ \ frac{pi}{3} -3x=pm frac{pi}{6}+2pi n,n in mathbb{Z}\ \ -3x=pm frac{pi}{6} -frac{pi}{3} +2pi n,n in mathbb{Z}~big|:(-3)\ \ boxed{x=mpfrac{pi}{18} +frac{pi}{} -frac{2pi n}{3},n in mathbb{Z} }$

$2)~3+4sin(2x+1)=0\ \ sin (2x+1)=- frac{3}{4} \ \ 2x+1=(-1)^{k+1}cdot arcsinfrac{3}{4}+ pi k,k in mathbb{Z}\ \2x=(-1)^{k+1}cdot arcsinfrac{3}{4}-1+pi k,k in mathbb{Z}~big|:2\ \ boxed{x= frac{(-1)^{k+1}cdot arcsinfrac{3}{4}}{2}- frac{1}{2} + frac{pi k}{2},k in mathbb{Z} }$