Question

(1+sint)(tgt+ctgt)(1-sint)

Answer 1

$(1+sint)(tgt+ctgt)(1-sint)=(1-sin^{2}t)(frac{sint}{cost}+frac{cost}{sint})=$

$=cos^{2}t*frac{sin^{2}t+cos^{2}t}{sint*cost}=cost*frac{1}{sint}=ctgt$