Question

Алгебра 10 класс
Решите уравнения

Answer 1

$1); ; cos5xcdot cos7x-sin5xcdot sin7x=-frac{sqrt3}{2}\\cos(5x+7x)=-frac{sqrt3}{2}\\12x=pm (pi -frac{pi }{6})+2pi n=pm frac{5pi }{6}+2pi n,; nin Z\\x=pm frac{5pi }{72}+frac{pi n}{6}; ,; nin Z\\2); ; sqrt3, cosx+sinx=1\\frac{sqrt3}{2}, cosx+frac{1}{2}, sinx=frac{1}{2}\\cos, frac{pi }{6}, cosx+sin, frac{pi }{6}, sinx=frac{1}{2}\\cos(x-frac{pi}{6})=frac{1}{2}\\x-frac{pi}{6}=pm frac{pi}{3}+2pi n,; nin Z\\x=frac{pi}{6}pm frac{pi }{3+2pi n,; nin Z$

$3); ; frac{tgfrac{pi}{5}-tg2x}{tgfrac{pi}{5}cdot tg2x+1}=sqrt3\\tg(frac{pi}{5}-2x)=sqrt3\\frac{pi}{5}-2x=frac{pi}{3}+pi n,; nin Z\\2x=-frac{2pi}{15}-pi n; ,; nin Z\\x=-frac{pi}{15}-frac{pi n}{15}, ,; nin Z$