Question

If \[\frac{{cosec}^2 \theta - \sec^2 \theta}{{cosec}^2 \theta + \sec^2 \theta}\]  write the value of \[\frac{1 - \cos^2 \theta}{2 - \sin^2 \theta}\] 

Answer 1

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`