Question

The value of \( \tan^{-1} \left( \frac{1}{2} \right) + \tan^{-1} \left( \frac{1}{3} \right) \) is

• A. \( \tan^{-1} 7 \)
• B. \( \tan^{-1} 15 \)
• C. \( \tan^{-1} 5 \)
• D. None of these

Hint:

Use the identity for the sum of two inverse tangents to simplify the expression.

Answer 1

The Correct Option is C

Use the identity \( \tan^{-1} a + \tan^{-1} b = \tan^{-1} \left( \frac{a + b}{1 - ab} \right) \) to simplify the expression.
Final Answer: \[ \boxed{\tan^{-1} 5} \]