Which of the following is the solution set of the equation $2 c o s^{- 1} x = c o t^{- 1} (\frac{2 x^{2} - 1}{2 x \sqrt{1 - x^{2}}})$

(0, 1)

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(- 1, 1) - {0}

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(- 1, 0)

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[- 1, 1]

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Solution

The correct option is B $(0, 1)$
$2 {c o s}^{- 1} x = {c o s}^{- 1} (2 x^{2} - 1)$ for $x ϵ [0, 1]$
And ${c o s}^{- 1} (2 x^{2} - 1) = {c o t}^{- 1} (\frac{2 x^{2} - 1}{2 x \sqrt{1 - x^{2}}})$ for $x ϵ (0, 1)$

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