Question

if `cosec A = sqrt2` find the value of `(2 sin^2 A + 3 cot^2 A)/(4(tan^2 A - cos^2 A))`

Answer 1

Given `cosec A = sqrt2`

We have to find the value of the expression  `(2 sin^2 A + 3 cot^2 A)/(4(tan^2 A - cos^2 A))`

We know that

`cosec A =sqrt2`

`=> sin A = 1/(cosec A) = 1/sqrt2`

`cos A = sqrt(1 - sin^2 A) = sqrt(1 - (1/sqrt2)^2) = 1/sqrt2`

`tan A = sin A/cos A = (1/sqrt2)/(1/sqrt2) = 1`

`cot A = 1/tan A = 1/1 = 1`

Therefore,

`(2 sin^2 A + 3 cot^2 A)/(4(tan^2 A - cos^2 A)) = (2 xx (1/sqrt2)^2 + 3 xx 1^2)/(4(1^2 - (1/sqrt2)^2))`

= 2

Hence, the value of the given expression is 2