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Complementary Trigonometric Ratios

In Δ ABC, a...

Question

In $Δ$ ABC, angle C is a right angle, then the value
of tan $A + t a n B$ is

t a n C

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c

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\frac{c}{a b}

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

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Solution

The correct option is C $\frac{c^{2}}{a b}$
$G i v e n A B C i s a t r i a n g l e w i t h C = 90^{\circ} ∴ a^{2} + b^{2} = c^{2} N o w t a n A = \frac{a}{b} - - - (1) a n d t a n B = \frac{b}{a} - - - (2) ∴ t a n A + t a n B = \frac{a}{b} + \frac{b}{a} = \frac{a^{2} + b^{2}}{a b} = \frac{c^{2}}{a b} p r o v e d .$

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