Question

((sint + cost)^2 - 1)(ctg - sint cost) = 2 tg^2t

Answer 1

$frac{(sint+cost)^2-1}{ctgt-sintcost}=frac{2cost*sint}{ctgt-sintcost}=frac{2cost*sint}{frac{cost}{sint}-sintcost} = frac{2costsin^2t}{cost-sin^2tcost}=frac{2sin^2t}{1-sin^2t}=frac{2sin^2t}{cos^2t}=2tg^2t$