Question

If \(\tan A = \dfrac{5}{6}\), \(\tan B = \dfrac{1}{11}\), then find \(A + B\).

• A. \(-\dfrac{\pi}{4}\)
• B. \(-\dfrac{\pi}{3}\)
• C. \(\dfrac{\pi}{3}\)
• D. \(\dfrac{\pi}{4}\)

Hint:

Always simplify the numerator and denominator separately while using tangent addition formula.

Answer 1

The Correct Option is D

Step 1: Use the tangent addition formula.
\[ \tan(A+B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \]
Step 2: Substitute the given values.
\[ \tan(A+B) = \frac{\frac{5}{6} + \frac{1}{11}}{1 - \frac{5}{6}\cdot\frac{1}{11}} = \frac{\frac{61}{66}}{\frac{61}{66}} = 1 \]
Step 3: Find \(A+B\).
\[ \tan(A+B) = 1 \Rightarrow A+B = \frac{\pi}{4} \]