CUET · MATHS · PYQ PAPER 2023
The simplest form of \(\tan ^{-1}\left(\frac{x}{\sqrt{a^2-x^2}}\right)\) is, where \(-a < x < a\).
- A \(\tan ^{-1} \frac{x}{a}\)
- B \(\tan ^{-1}(a x)\)
- C \(a \tan ^{-1} \frac{x}{a}\)
- D \(\sin ^{-1} \frac{x}{a}\)
Answer & Solution
Correct Answer
(D) \(\sin ^{-1} \frac{x}{a}\)
Step-by-step Solution
Detailed explanation
Let \(x = a \sin \theta\). \(\sin \theta = \frac{x}{a}\) \(\theta = \sin^{-1}\left(\frac{x}{a}\right)\) \(\tan ^{-1}\left(\frac{x}{\sqrt{a^2-x^2}}\right) = \tan ^{-1}\left(\frac{a \sin \theta}{\sqrt{a^2-(a \sin \theta)^2}}\right)\)…
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