Inverse Trigonometric Functions
Simplification
Premium Question
Grade 12
Question:
$\tan^{-1}\left(\frac{\sqrt{1 + x^2} - 1}{x}\right)$ for $x \neq 0$ simplifies to:
(1) $\frac{1}{2} \tan^{-1} x$
(2) $\tan^{-1} x$
(3) $\frac{1}{3} \tan^{-1} x$
(4) $2 \tan^{-1} x$
Step-by-Step Solution
Key Concept: Substitute $x = \tan \theta$. The expression inside becomes $\tan(\theta/2)$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)