Question

Даю 40 балов
2sin^2x+5sinx-3=0 ?

Answer 1

$\displaystyle 2sin^2x+5sinx-3=0\\\\sinx=t; |t|\leq 1\\\\2t^2+5t-3=0\\\\D=25+24=49\\\\t_{1.2}=\frac{-5 \pm 7}{4}\\\\t_1=\frac{1}{2}; t_2= -3$

t₂ не удовлетворяет

$\displaystyle sinx=\frac{1}{2}\\\\x_1=\frac{\pi}{6}+2\pi n; n \in Z\\\\x_2=\frac{5\pi}{6}+2\pi n; n \in Z$