In a triangle,if tan A + tan B + tan C = 6 an | vedclass

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(C) In any triangle $ABC$,the identity $	an A + 	an B + 	an C = 	an A 	an B 	an C$ holds true.Given $	an A + 	an B + 	an C = 6$ and $	an A \

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Both $(a)$ and $(b)$

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(C) In any triangle $ABC$,the identity $	an A + 	an B + 	an C = 	an A 	an B 	an C$ holds true.Given $	an A + 	an B + 	an C = 6$ and $	an A 	an B = 2$.Substituting these into the identity: $6 = 2 	an C \Rightarrow 	an C = 3$.Now,$	an A + 	an B = 6 - 	an C = 6 - 3 = 3$.We have the system $	an A + 	an B = 3$ and $	an A 	an B = 2$.The quadratic equation with roots $	an A$ and $	an B$ is $x^2 - 3x + 2 = 0$.Solving $(x - 1)(x - 2) = 0$,we get $x = 1$ or $x = 2$.Thus,the values are $(	an A, 	an B, 	an C) = (1, 2, 3)$ or $(2, 1, 3)$.

In a triangle,if $\tan A + \tan B + \tan C = 6$ and $\tan A \tan B = 2$,then the values of $\tan A, \tan B,$ and $\tan C$ are:

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