`tantheta+tan(9 0^(@)-theta)=secthetaxxsec(9 0^(@)-theta)`

Explanation

LHS= `tantheta+ tan(90^(@)-theta)` `[therefore tan(90^(@)-theta)=cot theta]`
`=tantheta + cot theta = (sintheta)/(costheta) +(costheta)/(sin theta)`
`=(sin^(2)theta+ cos^(2)theta)/(sinthetacostheta)` `[therefore tantheta=(sintheta)/(costheta)` and `cottheta=(costheta)/(sintheta)]`
`=1/(sinthetacostheta)` `[therefore sin^(2)theta+cos^(2)theta=1]`
`=sectheta"cosec"theta` `[therefore sectheta=1/(costheta)` and `costheta=1/(sintheta)]`
`=secthetasec(90^(@)-theta)=RHS` `[therefore sec(90^(@)-theta)="cosec"theta]`