In a `DeltaABC,` if median AD is perpendicular to AB, the `tan A+2 tan B` is equal to

Options

A. tan A + tan B = 0
B. 2 tan A + tan B = 0
C. tan A + 2tan B = 0
D. none of these

Answer

C

Explanation

We have BD = DC and `angle DAB = 90^(@)`. Draw CN perpendicular to BA produced, then in `Delta BCN`, we have `DA=(1)/(2)CN` and AB = AN

Let `angle CAN = alpha`
`because tan A = tan (pi - alpha)`
`= - tan alpha`
`=-(CN)/(NA)`
`=-2(AD)/(AB) (because Delta BAD ~ Delta BNC` and `AC = 2BD)`
`=-2 tan B`
`rArr tan A + 2 tan B = 0`