(A) In any $\triangle ABC$,the identity for the sum of tangents is $\tan A + \tan B + \tan C = \tan A \tan B \tan C$.Given that $\tan A + \tan B + \ta

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(A) In any $\triangle ABC$,the identity for the sum of tangents is $\tan A + \tan B + \tan C = \tan A \tan B \tan C$.Given that $\tan A + \tan B + \tan C = 6$,we have $\tan A \tan B \tan C = 6$.We are also given $\tan A \cdot \tan B = 2$.Substituting the value of $\tan A \cdot \tan B$ into the identity,we get $2 \cdot \tan C = 6$.Therefore,$\tan C = \frac{6}{2} = 3$.

Class 11 Mathematics Trigonometrical Equations Mix Examples-Trigonometrical Equations and Inequations, Properties of Triangles, Height and Distance

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In $\triangle ABC$,if $\tan A + \tan B + \tan C = 6$ and $\tan A \cdot \tan B = 2$,then $\tan C = \dots$

MHT CET 2019 All MHT CET

A
$3$
B
$4$
C
$1$
D
$2$

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Mix Examples-Trigonometrical Equations and Inequations, Properties of Triangles, Height and Distance

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In $\triangle ABC$,if $\tan A + \tan B + \tan C = 6$ and $\tan A \cdot \tan B = 2$,then $\tan C = \dots$

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