Докажите тождество

Решите задачу:

$( \frac{cost}{tgt}+ \frac{sint}{ctgt}):( \frac{sint}{cost} + \frac{cost}{sint}-1) = \\ \\ = ( \frac{cos^2t}{sint}+ \frac{sin^2t}{cost} ):( \frac{sin^2t+cos^2t-costsint}{cost*sint} )= \\ \\ = \frac{cos^3t+sin^3t}{sint*cost} * \frac{cost*sint}{sin^2t-costsint+cos^2t}= \\ \\ = \frac{(cost+sint)(sin^2t-costsint+cos^2t)}{sin^2t-costsint+cos^2t} =sint+cost$