Question

Prove `sqrt( sec^2theta+cosec^2theta)=tantheta+cottheta` ?

Answer 1

`LHS=sqrt( sec^2theta+cosec^2theta)`

`=sqrt(1+tan ^2theta+1+cot^2theta)`

`=sqrt(tan ^2theta+2+cot^2theta)`

`=sqrt(tan ^2theta+2tanthetacottheta+cot^2theta)`

`=sqrt((tan theta+cottheta)^2)`

`=tantheta+cottheta =RHS`