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If Sqrt3 Tan Theta = 3 Sin Theta` Find the Value of Sin^2 Theta - Cos^2 Theta - Mathematics

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

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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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APPEARS IN

RD Sharma Class 10 Maths
Chapter 11 Trigonometric Identities
Exercise 11.2 | Q 10 | Page 54
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