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Question
if `sqrt3 tan theta = 3 sin theta` find the value of `sin^2 theta - cos^2 theta`
Solution
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
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