Question

If `cot theta = sqrt3` find the value of `(cosec^2 theta + cot^2 theta)/(cosec^2 theta - sec^2 theta)`

Answer 1

Given: `cot theta = sqrt3`

We have to find the value of the expression `(cosec^2 theta + cot^2 theta)/(cosec^2 theta - sec^2 theta)`

We know that

`cot theta = sqrt3 => cot^2 theta = 3` 

`cosec^2 theta =1 + cot^2 theta = 1 + (sqrt3)^2 = 4`

`sec^2 theta = 1/cos^2 theta = 1/(1 - sin^2 theta) = 1/(1 - 1/(cosec^2 theta)) = 1/(1 - 1/4) = 4/3`

Therefore

`(cosec^2 theta + cot^2 theta)/(cosec^2 theta - sec^2 theta) = (4 + 3)/(4 - 4/3)`

`= 21/8`

Hence, the value of the given expression is `21/8`