Question

Решите уравнение 2sin(2x +п /5(дробь)) = √2

Answer 1

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Answer 2

$2 \sin \frac{2x + \pi}{5} = \sqrt{2} \\ \sin \frac{2x + \pi}{5} = \frac{ \sqrt{2} }{2} \\ \frac{2x + \pi}{5} = ( -1 ) {}^{n} \frac{\pi}{4} + \pi \: n \\ 2x + \pi = ( - 1) {}^{n} \frac{5\pi}{4} + 5\pi \: n \\ 2x = - \pi + ( - 1) {}^{n} \frac{5\pi}{4} + 5\pi \: n \\ x = - \frac{\pi}{2} + ( - 1) {}^{n} \frac{5\pi}{8} + \frac{5\pi}{2} n$

где n целое число