Question

sin15x+√3cos15x-2=0 ​

Answer 1

Пошаговое объяснение:

$2(\frac{1}{2} \times \sin15x + \frac{ \sqrt{3} }{2} \times \cos15x ) - 2 = 0$

$2( \cos\frac{\pi}{3} \sin15x + \frac{ \sqrt{3} }{2} \times \cos15x) - 2 = 0$

$2( \cos\frac{\pi}{3} \sin15x + sin\frac{\pi}{3} \cos15x) - 2 = 0$

$2 \sin(15x + \frac{\pi}{3} ) - 2 = 0$

$2 \sin(15x + \frac{\pi}{3} ) = 0 + 2$

$2 \sin(15x + \frac{\pi}{3} ) = 2$

$\sin(15x + \frac{\pi}{3} ) = 1$

$15x + \frac{\pi}{3} = \frac{\pi}{2 } + 2k\pi. \: k \: e \: z$

$15x = \frac{\pi}{2} - \frac{\pi}{3} + 2k\pi. \: k \: e \: z$

$15x = \frac{\pi}{6} + 2k\pi. \: k \: e \: z$

$x = \frac{\pi}{90} + \frac{2k\pi}{15} . \: k \: e \: z$