Question

Докажите тождество.
((sint+cost)^2-1)/(tgt-sint*cost)=2ctg^2t

Answer 1

Преобразуем левую часть.
$frac{(sint+cost)^2-1}{tgt-sint*cost}=frac{sin^2t+cos^2t+2sintcost-1}{frac{sint}{cost}-sint*cost}=frac{1+2sintcost-1}{sint(frac{1}{cost}-cost)}=frac{2cost}{frac{1-cos^2t}{cost}}=\=frac{2cos^2t}{sin^2t}=2ctg^2t$