If the median of △ABC through A is perpendicular to AB, then
A
tanA+tanB=0
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B
2tanA+tanB=0
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C
tanA+2tanB=0
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D
none of these
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Solution
The correct option is DtanA+2tanB=0 Applying m−n co-tangent theorem, to △ABC we have (a2+a2)cot(90+B) =a2cotπ2−a2cot(A−π2) ⇒−atanB=0+a2tanA ⇒−atanB=a2tanA ∴tanA+2tanB=0