If $(1 + cot^2 θ) + ( 1 + (cot^2 θ)^{-1})$ is equal to k, then $\sqrt{k}$ = ?

cosec θ sec θ

( 1 + cot²θ ) + {1 + (cot²θ)^-1}\)   = k

( 1 + cot²θ ) + ( 1 + tan²θ ) = k

{ we know, cosec²θ - cot²θ = 1   &  sec²θ - tan²θ = 1 
  }

cosec²θ  + sec²θ   = k

 \(\frac{sin²θ  + cos²θ }{ sin²θ.cos²θ }\)    = k

{ sin²θ  + cos²θ = 1 }

\(\frac{1 }{ sin²θ.cos²θ }\)    = k

cosec²θ.sec²θ = k

\(\sqrt {k }\) = cosecθ.secθ