What is the value of $\frac{cotθ+cosecθ-1}{cotθ-cosecθ+1}$
Answer & explanation
Correct answer: option 4
$\frac{cotθ+cosecθ-1}{cotθ-cosecθ+1}$
( Using, cosec²θ - cot²θ = 1 }
= $\frac{cotθ+cosecθ- (cosec²θ - cot²θ )}{cotθ-cosecθ+1}$
= $\frac{cotθ+cosecθ-[ (cosecθ - cotθ). (cosecθ +cotθ)]}{cotθ-cosecθ+1}$
= $\frac{cotθ+cosecθ-[ 1 - cosecθ +cotθ]}{cotθ-cosecθ+1}$
= cotθ+ cosecθ