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Question
If \[\frac{{cosec}^2 \theta - \sec^2 \theta}{{cosec}^2 \theta + \sec^2 \theta}\] write the value of \[\frac{1 - \cos^2 \theta}{2 - \sin^2 \theta}\]
Solution
Given: `cot θ=1/sqrt3`
`"Base"/"Perpendicular"=1/sqrt3`
`"Base"=1`
`"Perpendicular"=sqrt3`
`"Hypotenuse"= sqrt(("Perpendicular")^2+(Base)^2)`
`"Hypotenuse"=2`
Now we find, `(1-cos^2 θ)/(2- sin^2 θ)`
= `(1- ("Base")^2/("hypotenuse")^2)/ (2-("Perpendicular")^2/("hypotenuse")^2)`
=`(1-(1)^2/(2)^2)/(2-(sqrt3)^2/(2)^2)`
=`(1-1/4)/(2-3/4)`
=`3/5`
Hence the value of `(1-cos^2θ)/(2-sin^2θ)` is `3/5`
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