If $A + B + C = 180^{0},$ then $t a n A + t a n B + t a n C$ is equal to

2 tan A tan B tan C

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tan A tan B tan C

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cot A cot B cot C

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tan A tan B cot C

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Solution

The correct option is B tan A tan B tan C
We know, $A + B + C = 180^{0}$
or $A + B = 180^{0} - C$
$∴ t a n (A + B) = t a n (180^{0} - C)$
or $\frac{t a n A + t a n B}{1 - t a n A t a n B} = - t a n C$
or $t a n A + t a n B = - t a n C + t a n A t a n B t a n C$
or $t a n A + t a n B + t a n C = t a n A t a n B t a n C$

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