Question

Розв’язати рівняння: 2*cos(x - pi/4) + sqrt(3) = 0

Answer 1

Ответ:

$\boldsymbol{x_1 = \frac{13\pi}{12} + 2\pi n,n\in Z} \\ \boldsymbol{ x_2 = \frac{17\pi}{12} + 2 \pi k,k\in Z }$

Объяснение:

$\displaystyle 2 \cos\Big(x - \frac{\pi}{4} \Big) + \sqrt{3} = 0 \\ 2 \cos\Big(x - \frac{\pi}{4} ) = - \sqrt{3} |:2 \\ \cos\Big(x - \frac{\pi}{4} \Big) = - \frac{ \sqrt{3} }{2} \\ x - \frac{\pi}{4} = \frac{5\pi}{6} \\ x = \frac{5\pi}{6} + \frac{\pi}{4} + 2\pi n,n\in Z \\ \boldsymbol{x_1 = \frac{13\pi}{12} + 2\pi n,n\in Z} \\ x - \frac{\pi}{4} = \frac{7\pi}{6} \\ x = \frac{7\pi}{6} + \frac{\pi}{4} + 2 \pi k,k\in Z \\ \boldsymbol{ x_2 = \frac{17\pi}{12} + 2 \pi k,k\in Z }$