Question

Evaluate \( 2 \tan^{-1} \left( \frac{1}{3} \right) - \tan^{-1 \left( \frac{3}{4} \right) \)}

• A. 0
• B. 2
• C. 1
• D. 3

Hint:

When dealing with the sum or difference of arctangents, use the relevant identities to simplify the expressions.

Answer 1

The Correct Option is A

Step 1: Use the formula for the sum of arctangents.
The formula for the sum of two arctangents is: \[ \tan^{-1} x + \tan^{-1} y = \tan^{-1} \left( \frac{x + y}{1 - xy} \right) \] Using this formula, we can simplify the expression.
Step 2: Apply the formula.
We find that the value of the expression simplifies to \( 0 \).
Step 3: Conclusion.
The correct answer is (A) 0.