If $\begin{Bmatrix}\begin{pmatrix}\frac{sec θ−1}{sec θ+1}\end{pmatrix}\end{Bmatrix}^n = cosec θ − cot θ$ , then n = ?

0.5

{ ( \(\frac{secθ - 1 }{secθ + 1}\) ) }n = cosecθ - cot θ

Let us assume that , θ = 45º

{ ( \(\frac{sec 45º - 1 }{sec 45º + 1}\) ) }n = cosec 45º - cot  45º

{ ( \(\frac{√2 - 1 }{√2 + 1}\) ) }n = √2 - 1

Rationalizing on LHS

{ ( \(\frac{(√2 - 1)² }{2 - 1 }\) ) }n = √2 - 1

So, to satisfy the given equation .

n must be = 0.5