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If $A + B + C = π$ then the value of $\frac{\tan A + \tan B + \tan C}{\tan A . \tan B . \tan C} + \frac{\cot A}{\tan B} + \frac{\cot B}{\tan C} + \frac{\cot C}{\tan A}$

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detailed solution

Correct option is B

A+B+C=π⇒ tanA+tanB+tanC=tanAtanBtanC and cotAcotB+cotBcotC+cotCcotA=1⇒cotAtanB+cotBtanC+cotCtanA=1 ∴tanA+tanB+tanCtanAtanBtanC+cotAtanB+cotBtanC+cotCtanA=1+1=2

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If A+B+C=πthen the value of tanA+tanB+tanCtanA.tanB.tanC+cotAtanB+cotBtanC+cotCtanA

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If $A + B + C = π$ then the value of $\frac{\tan A + \tan B + \tan C}{\tan A . \tan B . \tan C} + \frac{\cot A}{\tan B} + \frac{\cot B}{\tan C} + \frac{\cot C}{\tan A}$