Question

(ctga/3-tga/3)*tg2a/3

Answer 1

$(ctg frac{ alpha }{3} -tg frac{ alpha }{3} )*tg2 frac{ alpha }{3}$
$tg2 frac{ alpha }{3} = frac{2tg frac{ alpha }{3} }{1-tg^2 frac{ alpha }{3} }$
$ctg frac{ alpha }{3} -tg frac{ alpha }{3} * frac{2tg frac{ alpha }{3} }{1-tg^2 frac{ alpha }{3} } = frac{2tg frac{ alpha }{3}(ctgfrac{ alpha }{3}-tgfrac{ alpha }{3}) }{1-tg^2frac{ alpha }{3}}$
$frac{2ctgfrac{ alpha }{3}*tgfrac{ alpha }{3}-2tg^2frac{ alpha }{3}}{1-tg^2frac{ alpha }{3}} = frac{2-2tg^2frac{ alpha }{3}}{1-tg^2frac{ alpha }{3}} = frac{2(1-tg^2frac{ alpha }{3})}{(1-tg^2frac{ alpha }{3})} =2$

*$tg alpha *ctg alpha = frac{sin alpha }{cos alpha } * frac{cos alpha }{sin alpha } =1$