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If $0 \leq x \leq 1$ , then
$\tan \{\frac{1}{2} \sin^{- 1} \frac{2 x}{1 + x^{2}} + \frac{1}{2} \cos^{- 1} \frac{1 - x^{2}}{1 + x^{2}}\}$ is equal to

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2x1−x2

2x1+x2

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Correct option is A

We know thatsin−1⁡2x1+x2=2tan−1⁡x, if −1≤x≤1and, cos−1⁡1−x21+x2=2tan−1⁡x, if 0≤x<∞∴ tan⁡12sin−1⁡2x1+x2+12cos−1⁡1−x21+x2= tan⁡2tan−1⁡x for 0≤x≤1= tan⁡tan−1⁡2x1−x2=2x1−x2

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If 0≤x≤1, thentan⁡12sin−1⁡2x1+x2+12cos−1⁡1−x21+x2 is equal to

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Ready to Test Your Skills?

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If $0 \leq x \leq 1$ , then
$\tan \{\frac{1}{2} \sin^{- 1} \frac{2 x}{1 + x^{2}} + \frac{1}{2} \cos^{- 1} \frac{1 - x^{2}}{1 + x^{2}}\}$ is equal to