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If tantheta=(1)/(2) and tanphi=(1)/(3),...

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

A

`(pi)/(6)`

B

`pi`

C

`0`

D

`(pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
D
Given that, `tantheta=(1)/(2) and t anphi=(1)/(3)`
Now, `" "tan(theta+phi)=(tantheta+tanphi)/(1-tantheta*tanphi)`
`rArr" "tan(theta+phi)=((1)/(2)+(1)/(3))/(1-(1)/(2)*(1)/(2))rArrtan(theta+phi)=((3+2)/(6))/((6-1)/(6))=(5)/(5)=1`
`rArr" "tan(theta+phi)=tan""(pi)/(4)`
`therefore" "theta+phi=(pi)/(4)`
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