Can there exist triangles ABC satisfying the following relations? Write yes or no giving reasons:
tanA +tanB+tanC =0

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Solution

No. since $A + B + C$ = $π$
$∴$ $\sum t a n A = t a n A t a n B t a n C = 0$
$\Rightarrow$ Either $A = 0 o r B = 0 o r C = 0$
Which is not possible in a triangle.

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