If in $△ A B C, ∠ A = 90^{0}, B C = a, A C = b a n d A B = c,$ then the value of tan B + tan C is

\frac{c^{2}}{a b}

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\frac{a^{2} + c^{2}}{b}

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\frac{b^{2}}{a c}

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\frac{a^{2}}{b c}

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Solution

The correct option is D $\frac{a^{2}}{b c}$
$t a n B = \frac{A C}{A B} = \frac{b}{c}$

$t a n C = \frac{A B}{A C} = \frac{c}{b}$

$t a n B + t a n C = \frac{b}{c} + \frac{c}{b} = \frac{b^{2} + c^{2}}{b c} = \frac{a^{2}}{b c}$

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