Question

4) корень из 3 ctg (п/3 - x) = 3 5) 3 sin^2 x = cos^2 x

Answer 1

$\sqrt{3} ctg( \frac{\pi}{3} -x)=3|: \sqrt{3} \\ ctg( \frac{\pi}{3} -x)= \sqrt{3} \\ \frac{\pi}{3} -x=arcctg\sqrt{3} +\pi n,n \in Z \\ \frac{\pi}{3} -x= \frac{\pi}{6} + \pi n,n \in Z \\ -x=\frac{\pi}{6}-\frac{\pi}{3} + \pi n,n \in Z \\ \boxed{x=\frac{\pi}{6}-\pi n,n \in Z}$

$3\sin^2x=\cos^2x|:\cos^2x \\ 3 \frac{\sin^2x}{\cos^2x} = \frac{\cos^2x}{\cos^2x} \\ \\ 3tg^2x=1 \\ tg^2x= \frac{1}{ 3 } \\ \\ tg x=\pm \frac{1}{\sqrt{3}} \\ \\ x_1_,_2=\pm \frac{\pi}{6} +\pi n,n \in Z$