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If $\sin^{- 1} (\frac{2 x}{1 + x^{2}}) + \cos^{- 1} (\frac{1 - x^{2}}{1 + x^{2}}) = 4 \tan^{- 1} x,$ then

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x∈−(−∞,−1)

x∈(1,∞)

x∈[0,1]

x∈[−1,0)

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detailed solution

Correct option is C

We know that sin−1⁡2x1+x2=2tan−1⁡x for all x∈[−1,1]and, cos−1⁡1−x21+x2=2tan−1⁡x for all x∈[0,∞) ∴ sin−1⁡2x1+x2+cos−1⁡1−x21+x2=4tan−1⁡x for all x∈[0,1]

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If sin−1⁡2x1+x2+cos−1⁡1−x21+x2=4tan−1⁡x, then

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Ready to Test Your Skills?

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If $\sin^{- 1} (\frac{2 x}{1 + x^{2}}) + \cos^{- 1} (\frac{1 - x^{2}}{1 + x^{2}}) = 4 \tan^{- 1} x,$ then