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`

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