Question

Sin(x+pi/3)=1/2 Cos(x-pi/6)=корень 2/2 Ctg(x+pi/2)=-1

Answer 1

$sin(x+ \frac{ \pi }{3})= \frac{1}{2}\\x+ \frac{ \pi }{3}= \frac{ \pi }{6} +2 \pi k\\x=-\frac{ \pi }{6}+2 \pi k\\\\cos(x-\frac{ \pi }{6})= \frac{ \sqrt{2} }{2}\\x-\frac{ \pi }{6}= \frac{ \pi }{4} +2 \pi k\\x=\ \frac{5 \pi }{12} +2 \pi k\\\\ctg(x+ \frac{ \pi }{2})=-1\\x+ \frac{ \pi }{2}= \frac{ 3\pi }{4}+ \pi k\\x=\ \frac{ \pi }{4}+ \pi k$