Question

решите тригонометрическое уравнение sin(40+x)sin(x-50)=1
Пж решите

Answer 1

$sin(40+x)\cdot sin(x-50)=1\\\\\star \; \; sin(90-\alpha )=cos\alpha \; \; ;\; \; sin(40+x)=sin(90-(50-x))=cos(50-x)\; \star \\\\cos(50-x)\cdot sin(x-50)=1\\\\\star \; \; cos(-\alpha )=cos\alpha \; \; \star \\\\cos(x-50)\cdot sin(x-50)=1\\\\\star \; \; 2\cdot sin\alpha \cdot cos\alpha =sin2\alpha \; \; \star \\\\\frac{1}{2}\cdot sin(2x-100)=1\\\\sin(2x-100)=2\; \; \; \Rightarrow \; \; \; \boxed {x\in \varnothing }\\\\tak\; kak\; \; \; \; -1\leq sin(2x-100)\leq 1$