Question

If $ \tan^{-1}(x) = \tan^{-1}\left( 3 - \frac{\pi}{4} \right) $, find $ x $.

• A. \( 3 - \frac{\pi}{4} \)
• B. \( \frac{\pi}{4} - 3 \)
• C. \( 3 + \frac{\pi}{4} \)
• D. \( 3 - \frac{\pi}{2} \)

Hint:

If \( \tan^{-1}(x) = \tan^{-1}(y) \), then \( x = y \).

Answer 1

The Correct Option is A

We are given that: \[ \tan^{-1}(x) = \tan^{-1}\left( 3 - \frac{\pi}{4} \right) \] Since \( \tan^{-1}(x) \) gives the angle whose tangent is \( x \), the above equation implies: \[ x = 3 - \frac{\pi}{4} \] 
Thus, the value of \( x \) is \( 3 - \frac{\pi}{4} \).