If `tantheta=(1)/(2) and tanphi=(1)/(3)`, then the value of `theta+phi` is

Options

A. 0
B. `(pi)/(6)`
C. `(pi)/(4)`
D. `(pi)/(2)`

Answer

C

Explanation

`tantheta=(1)/(2)`
`tanphi=(1)/(3)`
`tan(theta+phi)=(tantheta+tanphi)/(1-tanthetatanphi)`
`=((1)/(2)+(1)/(3))/(1((1)/(2))((1)/(3)))=((5)/(6))/(6/(5))=1`
`thereforetheta+phi=tan^(-1)(1)=(pi)/(4)`