Question

Доказать тождество sin^3t*(1+ctgt)+cos^3t*(1+tgt)=sint+cost помогите

Answer 1

$sin^3t(1+ctgt)+cos^3t(1+tgt)=\\=sin^3tcdot (1+ frac{cost}{sint} )+cos^3tcdot (1+frac{sint}{cost})=\\=sin^3tcdot frac{sint+cost}{sint} +cos^3tcdot frac{sint+cost}{cost} =\\=sin^2t(sint+cost)+cos^2t(sint+cost)=\\=(sint+cost)(underbrace {sin^2t+cos^2t}_{1})=sint+cost$