Question

What is the value of \[\frac{\tan^2 \theta - \sec^2 \theta}{\cot^2 \theta - {cosec}^2 \theta}\]

Answer 1

We have, 

\[\frac{\tan^2 \theta - \sec^2 \theta}{\cot^2 \theta - {cosec}^2 \theta}\]=` (-1(sec ^2 θ-tan ^2θ ))/(-1 (cosec^2 θ-cot ^2 θ))` 

=`( secx^2θ-tan^2 θ)/ (cosec ^2 θ-cot^2 θ)` 

We know that, 

`sec^2θ-tan ^2θ=1` 

` cosec^2 θ-cot ^2θ=1`

Therefore, 

 `(tan ^2θ-sec^2 θ)/(cot^2θ-cosec^2 θ)=1/1`

=1