6 ctg(43п/18) - 4 tg(п/9)

[latex]6ctg( \frac{43 \pi}{18} )-4tg( \frac{ \pi }{9} )=6ctg( \frac{180*43}{18} } )-4tg( \frac{ 180 }{9} )=6ctg(430)-4tg(20)=[/latex][latex]6ctg(2*180+70)-4tg(20)=6ctg(70)-4tg(20)=[/latex][latex]6ctg(90-70)-4tg(20)=6tg20-4tg20=2tg20[/latex]

[latex]6ctg \frac{43\pi }{18} -4tg \frac{\pi }{9}=6ctg(2\pi + \frac{7\pi }{18} ) -4tg \frac{\pi }{9} =6ctg \frac{7\pi }{18} -4tg\frac{2\pi}{18}=\\\\=(\frac{7\pi}{18}+\frac{2\pi}{18}=\frac{9\pi}{18}=\frac{\pi}{2})=\\\\=6ctg(\frac{\pi}{2}-\frac{2\pi}{18})-4tg\frac{2\pi}{18}=6tg\frac{2\pi}{18}-4tg\frac{2\pi}{18}=2tg\frac{\pi}{9}[/latex]