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