COMEDK · Maths · 23. Inverse Trigonometric Functions
The range of \(x\) for which the equation \(\sin ^{-1}\left(\dfrac{2 x}{1+x^2}\right)=2 \tan ^{-1} x\) holds true
- A \(x \geq 0\)
- B \(\forall x \in R\)
- C \(|x| \geq 1\)
- D \(|x| \leq 1\)
Answer & Solution
Correct Answer
(D) \(|x| \leq 1\)
Step-by-step Solution
Detailed explanation
The expression \(\sin^{-1}\left(\dfrac{2x}{1+x^2}\right)\) is defined for \(\left|\dfrac{2x}{1+x^2}\right| \leq 1\), which implies \(2|x| \leq 1+x^2\), or \((|x|-1)^2 \geq 0\), which is true for all \(x \in R\). Recall the identity…
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