Question

Помогите найти tg(a-π/6) ,если ctg a =1/√2

Answer 1

$tg( alpha - frac{ pi }{6})= frac{tg alpha -tg frac{ pi }{6} }{1+tg alpha tg frac{ pi }{6} } \\tg alpha = frac{1}{Ctg alpha } = frac{1}{ frac{1}{ sqrt{2} } } = sqrt{2} \\tg frac{ pi }{6}= frac{ sqrt{3} }{3} \\\tg( alpha - frac{ pi }{6})= frac{ sqrt{2} - frac{ sqrt{3} }{3} }{1+ sqrt{2}* frac{ sqrt{3} }{3} } = frac{ frac{3 sqrt{2}- sqrt{3} }{3} }{1+ frac{ sqrt{6} }{3} } = frac{3 sqrt{2}- sqrt{3} }{3+ sqrt{6} } =$$= frac{ sqrt{3}( sqrt{6}-1) }{ sqrt{3}( sqrt{3} - sqrt{2}) } = frac{ sqrt{6}-1 }{ sqrt{3}- sqrt{2} }$