Answer 1

We have, 

`cosec^2 (90°-θ)- tan ^2θ= {cosec(90°-θ)}^2-tan ^2θ` 

                               = `(secθ )^2-tan^2 θ` 

                             = `sec^2 θ-tan ^2 θ` 

We know that, ` sec^2 θ-tan ^2θ=1` 

Therefore, \[{cosec}^2 \left( 90° - \theta \right) - \tan^2 \theta = 1\]