What is the value of tan^2θ - sec^2θ/cot^2θ - cosec^2θ?

Question

What is the value of \(\frac{tan^2θ - sec^2θ}{cot^2θ - cosec^2θ}\) ?

Answer 1

To find:  \(\frac{tan^2θ - sec^2θ}{cot^2θ - cosec^2θ}\)

We know that 1 + tan²θ = sec²θ 

And 1 + cot²θ = cosec²θ 

⇒ tan²θ – sec²θ = – 1 

And cot²θ – cosec²θ = – 1

⇒ \(\frac{tan^2θ - sec^2θ}{cot^2θ - cosec^2θ}\) = \(\frac{-1}{-1}\) = 1