Question

Решите тригонометрическое уравнение
sin2x+sin^2x=0

Answer 1

$\sin(2x)+\sin^2x=0\\\sin^2 x+2\sin x\cos x=0\div \sin^2 x\neq 0\\1+2\cot x=0\\\\\cot x = -\dfrac{1}{2} \\x= \text{arcctg} \bigg(\!-\dfrac{1}{2} \bigg)+ \pi n, n \in Z\\\\x=\pi-\text{arcctg}\bigg(\!-\dfrac{1}{2} \bigg)+\pi n, n \in Z$