KCET · Maths · Trigonometric Ratios & Identities
If \(\triangle A B C\) is right angled at \(C\), then the value of \(\tan A+\tan B\) is
- A \(a+b\)
- B \(a^2 / b c\)
- C \(c^2 / a b\)
- D \(b^2 / a c\)
Answer & Solution
Correct Answer
(C) \(c^2 / a b\)
Step-by-step Solution
Detailed explanation
\(\because \tan A=\frac{a}{b}, \tan B=\frac{b}{a}\)
\(\therefore \quad \tan A+\tan B=\frac{a}{b}+\frac{b}{a}\)
\(=\frac{a^2+b^2}{a b}\)
\(=\frac{c^2}{a b} \quad\left[\because c^2=a^2+b^2\right]\)
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