Question

If $\tan A = \frac{1}{2}$ and $\tan B = \frac{1}{3}$, then $A+B =$

• A. $30^{\circ}$
• B. $45^{\circ}$
• C. $60^{\circ}$
• D. $90^{\circ}$

Hint:

If you see $1/2$ and $1/3$ for tangents, the answer is almost always $45^{\circ}$!

Answer 1

The Correct Option is B

Step 1: Concept
Use the compound angle formula: $\tan(A+B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$.

Step 2: Meaning
We substitute the given values into the formula to find the tangent of the sum of the angles.

Step 3: Analysis
$\tan(A+B) = \frac{1/2 + 1/3}{1 - (1/2 \cdot 1/3)} = \frac{5/6}{1 - 1/6} = \frac{5/6}{5/6} = 1$.

Step 4: Conclusion
Since $\tan(A+B) = 1$, the angle $A+B$ must be $45^{\circ}$ (or $\pi/4$).
Final Answer: (B)