Question:
If $\tan^{-1}x = \tan^{-1}(3) - \frac{\pi}{4}$, then $x$ is equal to:
If $\tan^{-1}x = \tan^{-1}(3) - \frac{\pi}{4}$, then $x$ is equal to:
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Always replace constants like $\pi/4$ with their inverse trig equivalent to match the equation structure.
Updated On: Apr 28, 2026
- $\frac{1}{2}$
- $\frac{1}{4}$
- 1
- 3
- 2
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Note that $\frac{\pi}{4} = \tan^{-1}(1)$.
Step 2: Analysis
$\tan^{-1} x = \tan^{-1}(3) - \tan^{-1}(1)$. Use the formula $\tan^{-1} a - \tan^{-1} b = \tan^{-1}(\frac{a-b}{1+ab})$.
Step 3: Calculation
$x = \frac{3 - 1}{1 + (3 \cdot 1)} = \frac{2}{4} = \frac{1}{2}$. Final Answer: (A)
Note that $\frac{\pi}{4} = \tan^{-1}(1)$.
Step 2: Analysis
$\tan^{-1} x = \tan^{-1}(3) - \tan^{-1}(1)$. Use the formula $\tan^{-1} a - \tan^{-1} b = \tan^{-1}(\frac{a-b}{1+ab})$.
Step 3: Calculation
$x = \frac{3 - 1}{1 + (3 \cdot 1)} = \frac{2}{4} = \frac{1}{2}$. Final Answer: (A)
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