triangle A B C is right angled at C, then tan A+ tan B is equal to

Question

triangle A B C is right angled at C, then tan A+ tan B is equal to (A) (b2/a c) (B) a+b (C) (a2/b c) (D) (c2/a b)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/06f61719fa692935127d1660565941eb-.png" /> tan A=(a/b), tan B=(b/a) ∴ tan A+ tan B=(a2+b2/a b) Since, a2+b2=c2 ∴ tan A+ tan B=(c2/a b)

Q. $△ A BC$ is right angled at $C$ , then $tan A + tan B$ is equal to

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

$a + b$

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

$\frac{c ^{2}}{ab}$

$tan A = \frac{a}{b}, tan B = \frac{b}{a}$
$∴ tan A + tan B = \frac{a ^{2} + b ^{2}}{ab}$
Since, $a^{2} + b^{2} = c^{2}$
$∴ tan A + tan B = \frac{c ^{2}}{ab}$

Q. △ABC is right angled at C, then tanA+tanB is equal to

acb2​

a+b

bca2​

abc2​