Question

Решите уравнение:

3tg(x - п\7)=√3

Answer 1

$\displaystyle\bf\\3tg\Big(x-\frac{\pi }{7}\Big)=\sqrt{3} \\\\\\tg\Big(x-\frac{\pi }{7}\Big)=\frac{\sqrt{3} }{3} \\\\\\x-\frac{\pi }{7}=arctg\frac{\sqrt{3} }{3} +\pi n,n\in Z\\\\\\x-\frac{\pi }{7}=\frac{\pi }{6} +\pi n,n\in Z\\\\\\x=\frac{\pi }{6} +\frac{\pi }{7} +\pi n,n\in Z\\\\\\x=\frac{13\pi }{42} +\pi n,n\in Z$