Question

6 ctg(43п/18) - 4 tg(п/9)

Answer 1

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

Answer 2

$6ctg frac{43pi }{18} -4tg frac{pi }{9}=6ctg(2pi + frac{7pi }{18} ) -4tg frac{pi }{9} =6ctg frac{7pi }{18} -4tgfrac{2pi}{18}=\\=(frac{7pi}{18}+frac{2pi}{18}=frac{9pi}{18}=frac{pi}{2})=\\=6ctg(frac{pi}{2}-frac{2pi}{18})-4tgfrac{2pi}{18}=6tgfrac{2pi}{18}-4tgfrac{2pi}{18}=2tgfrac{pi}{9}$