If `sqrt3 tan theta=3 sin theta` then the value of (`sin^(2)theta-cos^(2)theta)` is

Options

A. 1
B. 3
C. `(1)/(3)`
D. none of these

Answer

c

Explanation

`sqrt(3)tantheta=3sin theta`
shortcut method
`sqrt(3)(sin theta)/(cos theta)=3sin theta`
`sqrt(3)/(cos theta)=3`
`cos theta=sqrt(3)/(3)`
then perpendicular `=sqrt(6)`

`(sin ^(2)theta-cos^(2)theta)`
`rArr((sqrt(6))/(H))^(2)-((B)/(H))^(2)`
`rArr (6)/(9)-(3)/(9)=(1)/(3)`