Sin^3t(1+ctgt) + cos^3t(1+tgt) = sint+cost

Question

Sin^3t(1+ctgt) + cos^3t(1+tgt) = sint+cost

Answer 1

sin^3t+sin^2tcost+cos^3t+cos^2tsint=(sint+cost)(1-sintcost)+costsint(sint+cost)=

=(sint+cost)(1-sintcost+sintcost)=sint+cost