prove that : cosQ/ 1-tanQ + sinQ/1-cotQ = sinQ + cosQ - Maths - Introduction to Trigonometry

Question

prove that : cosQ/ 1-tanQ + sinQ/1-cotQ = sinQ + cosQ

Nakush · Accepted Answer

cosQ/1-tanQ +sinQ/1-cotQ = sinQ + cosQ
L H S= cosQ/ 1- (sinQ/cosQ) + sinQ/ 1-(cosQ/sinQ)
=cos2Q / (cosQ-sinQ) + sin2Q /
(sinQ-cosQ)
=cos2Q / (cosQ-sinQ) - sin2Q /
(cosQ-sinQ)
=cos2Q-sin2Q / (cosQ- sinQ)
=(cosQ+sinQ)(cosQ-sinQ) / (cosQ- sinQ)
= cosQ+sinQ
L H S=R H S