Prove the following identity, where the angles involved are acute angles for which the expressions are defined.(iii) `(tantheta)/(1-cottheta)+(cottheta)/(1-tantheta)=1+sectheta cosectheta`

Prove the following identity, where the angles involved are acute angl

1.	Prove the following identity, where the angles involved are acute angles for which the expressions are defined.(iii) `(tantheta)/(1-cottheta)+(cottheta)/(1-tantheta)=1+sectheta cosectheta`
Answer» Left hand side =`(tantheta)/(1-cottheta)+(cottheta)/(1-tantheta)` =`(tantheta)/(1-cottheta)+(cottheta)/(1-tantheta)` =`(-tantheta)/(1-tantheta)+(cottheta)/(1-tantheta)` =`(-tan^2theta+tantheta)/(1-tantheta)` =`1/tantheta((1-tan^3theta)/(1-tantheta))` =`1/tantheta(1+tan^2theta+tantheta)` =`1+seccthetacosectheta`