Question

Помогите , дам хорошие баллы )))срочно !

Answer 1

$1.;2sin3x=sqrt3\sin3x=frac{sqrt3}2\3x=(-1)^ncdotfracpi3+pi n\x=(-1)^ncdotfracpi9+frac{pi n}3\x_{min}=fracpi9+frac{2pi}3=frac{7pi}9\\2.;cos x=-frac{sqrt3}2\x=pmfrac{5pi}6+2pi n\xin[pi;;frac{3pi}2]:\x=-frac{5pi}6+2pi=frac{7pi}6\\3.;sinfrac{pi(x+1)}{12}=-frac12\frac{pi(x+1)}{12}=(-1)^ncdotfrac{7pi}6+pi n\x+1=(-1)^ncdot14+12n\x=(-1)^ncdot14+12n-1$

$4.;sin(pi-x)-cos(fracpi2+x)=sqrt3\sin x+sin x=sqrt3\2sin x=sqrt3\sin x=frac{sqrt3}2\x=(-1)^ncdotfracpi3+pi n\\5.;cos2xcos x-sin2xsin x=-frac12\frac12(cos x+cos3x-cos x+cos3x)=-frac12\2cos3x=-1\cos3x=-frac12\3x=pmfrac{2pi}3+2pi n\x=pmfrac{2pi}9+frac{2pi n}3\xin[50^o;;120^o]:\x=-frac{2pi}9+frac{2pi}3=-40^o+120^o=80^o$
$6.;4sin xcos x=-sqrt3\2sin2x=-sqrt3\sin2x=-frac{sqrt3}2\2x=(-1)^ncdotfrac{4pi}3+pi n\x=(-1)^ncdotfrac{2pi}3+frac{pi n}2\x_{min}=-frac{2pi}3+frac{3pi}2=-120^o+270^o=150^o$