1.

If `tanA=(1)/(2) and tanB=(1)/(3)`, then `tan(2A+B)` is equal toA. 1B. 2C. 3D. 4

Answer» Correct Answer - C
Given that, `tanA=(1)/(2) and tanB=(1)/(3)`
Now, `" "tan(2A+B)=(tan2A+tanB)/(1-tan2A*tanB)" "...(i)`
`Also, " "tan2A=(2tanA)/(1-tan^(2)A)=(2*(1)/(2))/(1-(1)/(4))=(4)/(3)`
From Eq. (i), ` tan(2A+B)=((4)/(3)+(1)/(3))/(1-(4)/(3)*(1)/(3))=((4)/(3)+(1)/(3))/((9-4)/(9))=((5)/(3))/((5)/(9))=3`


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