Question

If `sqrt3 tan theta = 3 sin theta`, find the value of `sin^2 theta - cos^2 theta`

Answer 1

Given: `sqrt3 tan theta = 3 sin theta`

We have to find the value of `sin^2 theta -cos^2 theta`.

`sqrt3 tan theta = 3 sin theta`

`=> sqrt3 sin theta/cos theta = 3 sin theta`

`=> cos theta = sqrt3/3 = 1/sqrt3`

Therefore,

`sin^2 theta - cos^2 theta = 1 - cos^2 theta - cos^2 theta`           (since, `sin^2 theta + cos^2 theta = 1`)

`= 1 - 2 cos^2 theta`

`= 1 - 2 xx (1/sqrt3)^2`

`= 1/3`

Hence, the value of the expression is `1/3`.