Question:
If $\tan \alpha = \dfrac{5}{6}$ and $\tan \beta = \dfrac{1}{11}$, where $0<\alpha,\beta<\dfrac{\pi}{2}$ then $\alpha + \beta =$:
If $\tan \alpha = \dfrac{5}{6}$ and $\tan \beta = \dfrac{1}{11}$, where $0<\alpha,\beta<\dfrac{\pi}{2}$ then $\alpha + \beta =$:
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If $\tan(\theta)=1$, then $\theta = \frac{\pi}{4}$ in first quadrant.
Updated On: Apr 24, 2026
- $\frac{\pi}{6}$
- $\frac{\pi}{2}$
- $\frac{\pi}{3}$
- $\frac{\pi}{4}$
- $\frac{2\pi}{3}$
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The Correct Option is D
Solution and Explanation
Concept:
• $\tan(\alpha + \beta) = \dfrac{\tan\alpha + \tan\beta}{1 - \tan\alpha \tan\beta}$
Step 1: Apply formula
\[ \tan(\alpha + \beta) = \frac{\frac{5}{6} + \frac{1}{11}}{1 - \frac{5}{6}\cdot\frac{1}{11}} \]
Step 2: Simplify numerator
\[ \frac{5}{6} + \frac{1}{11} = \frac{55 + 6}{66} = \frac{61}{66} \]
Step 3: Simplify denominator
\[ 1 - \frac{5}{66} = \frac{61}{66} \]
Step 4: Compute value
\[ \tan(\alpha + \beta) = \frac{61/66}{61/66} = 1 \]
Step 5: Find angle
\[ \alpha + \beta = \frac{\pi}{4} \] Final Conclusion:
\[ = \frac{\pi}{4} \]
• $\tan(\alpha + \beta) = \dfrac{\tan\alpha + \tan\beta}{1 - \tan\alpha \tan\beta}$
Step 1: Apply formula
\[ \tan(\alpha + \beta) = \frac{\frac{5}{6} + \frac{1}{11}}{1 - \frac{5}{6}\cdot\frac{1}{11}} \]
Step 2: Simplify numerator
\[ \frac{5}{6} + \frac{1}{11} = \frac{55 + 6}{66} = \frac{61}{66} \]
Step 3: Simplify denominator
\[ 1 - \frac{5}{66} = \frac{61}{66} \]
Step 4: Compute value
\[ \tan(\alpha + \beta) = \frac{61/66}{61/66} = 1 \]
Step 5: Find angle
\[ \alpha + \beta = \frac{\pi}{4} \] Final Conclusion:
\[ = \frac{\pi}{4} \]
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