Which one of the following is one of the solutions of the equation of the equation `tantheta=1`?

Options

A. `pi//2`
B. `pi//6`
C. `pi//4`
D. `pi//3`

Answer

B

Explanation

`tan2theta.tantheta=1`
`rArr(2tantheta)/(1-tan^(2)theta).tantheta=1`
`rArr2tan^(2)theta=1-tan^(2)thetarArr3tan^(2)theta=1`
`rArrtan^(2)theta=(1)/(3)=((1)/(sqrt(3)))^(2)`
`rArrtan^(2)theta=tan^(2)(30^(@))=tan^(2)((pi)/(6))[becausetheta=npi+-(pi)/(6)]`
`thereforetheta=(pi)/(6)`