Question

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)`

Answer 1

Correct Answer - 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)`