Question

Решите тригонометрическое уравнение.

Answer 1

Ответ:

$\sin {}^{2} ( \frac{x}{4} ) - \cos {}^{2} ( \frac{x}{4} ) = \frac{1}{2} \\ - ( \cos {}^{2} ( \frac{x}{4} ) - \sin {}^{2} ( \frac{x}{4} ) ) = \frac{1}{2} \\ - \cos(2 \times \frac{x}{4} ) = \frac{1}{2} \\ \cos( \frac{x}{2} ) = - \frac{1}{2} \\ \frac{x}{2} = \pm \frac{2\pi}{3} + 2\pi \: n \\ x = \pm \frac{4\pi}{3} + 4\pi \: n \\n \in \:Z$