Question

Sin(5x-p/6)=sin3x решить уравнение​

Answer 1

Применяем формулу разности синусов.

$sin(5x-\frac{\pi}{6})=sin3x\\\\sin(5x-\frac{\pi}{6})-sin3x=0\\\\2\cdot sin(x-\frac{\pi}{12})\cdot cos(4x-\frac{\pi}{12})=0\\\\a)\; \; sin(x-\frac{\pi}{12})=0\; \; ,\; \; x-\frac{\pi}{12}=\pi n\; ,\; n\in Z\\\\x=\frac{\pi}{12}+\pi n\; ,\; n\in Z\\\\b)\; \; cos(4x-\frac{\pi}{12})=0\; \; ,\; \; 4x-\frac{\pi}{12}=\frac{\pi}{2}+\pi k\; ,\; k\in Z\\\\4x=\frac{7\pi }{12}+\pi k\; ,\; \; x=\frac{7\pi}{48}+\frac{\pi k}{4}\; ,\; k\in Z\\\\x=\frac{7\pi}{48}+\frac{\pi k}{4}\; ,\; k\in Z$

$Otvet:\; \; x_1=\frac{\pi}{12}+\pi n\; ,\; \; x_2=\frac{7\pi}{48}+\frac{\pi k}{4}\; ,\; \; n,k\in Z\; .$

Answer 2

$x = \frac{\pi }{12}$

Объяснение:

$sin(5x-\frac{\pi }{6} )=sin3x$

$5x - \frac{\pi }{6} = 3x$

$5x - \frac{\pi }{6} - 3x = 0$

$2x - \frac{\pi }{6} = 0$

$2x = \frac{\pi }{6}$

$\frac{2x}{2} = \frac{\pi }{6} * \frac{1}{2}$

$x = \frac{\pi }{6} * \frac{1}{2}$

$x = \frac{\pi }{12}$

ответ: $x = \frac{\pi }{12}$