If `sqrt(3)tantheta=1` then find value of `sin^2theta-cos^2theta`

Options

A. `-1/2`
B. `1/2`
C. `1`
D. None

Answer

A

Explanation

Given that,
`sqrt(3)tantheta=1`
`rArr tantheta=1/sqrt(3) = tan 30^(@)`
`rArr theta=30^(@)`
Now, `sin^(2)theta-cos^(2)theta= sin^(2)30^(@)- cos^(2) 30^(@)`
`=(1/2)^(2)-(sqrt(3)/2)^(2)`
`1/4-3/4=(1-3)/4=-2/4=-1/2`