Question

sin(3z) - cos(3z) = sqrt(3) / 2

Answer 1

Ответ:

$z=\frac{\pi}{12}+\frac{1}{3} *(-1)^{k}arcsin\frac{\sqrt{6} }{4}+\frac{k\pi}{3}$  , k=0,±1, ±2, ...

Пошаговое объяснение:

$sin3z-cos3z=\frac{\sqrt{3} }{2} \\cos\frac{\pi}{4} sin3z-sin\frac{\pi}{4} cos3z=\frac{\sqrt{3} }{2}*\frac{\sqrt{2} }{2}\\sin(3z-\frac{\pi}{4})=\frac{\sqrt{6} }{4}\\3z-\frac{\pi}{4}=(-1)^{k}arcsin\frac{\sqrt{6} }{4}+k\pi \\3z=\frac{\pi}{4}+(-1)^{k}arcsin\frac{\sqrt{6} }{4}+k\pi\\z=\frac{\pi}{12}+\frac{1}{3} *(-1)^{k}arcsin\frac{\sqrt{6} }{4}+\frac{k\pi}{3}$