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: $6 = 2 	imes 	an C$.Therefore,$	an C = \frac{6}{2} = 3$.Now,we have $	an A + 	an B = 6 - 	an C = 6 - 3 = 3$.We are given $	an A 	an B = 2$.Let $	an A$ and $	an B$ be the roots of the quadratic equation $x^2 - (	an A + 	an B)x + 	an A 	an B = 0$.Substituting the values: $x^2 - 3x + 2 = 0$.Factoring the equation: $(x - 1)(x - 2) = 0$.Thus,the roots are $x = 1$ and $x = 2$.So,the set of values ${	an A, 	an B, 	an C}$ is ${1, 2, 3}$.This corresponds to both $(a)$ and $(b)$.

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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