Which of the following is the solution set of the equation $2 {cos}^{- 1} (x) = {cot}^{- 1} (\frac{2 x^{2} - 1}{2 x \sqrt{1 - x^{2}}})$ ?

(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 A $(0, 1)$
$2 c o s^{- 1} (x) = c o s^{- 1} (2 x^{2} - 1)$ for $x ϵ [0, 1]$
$\Rightarrow c o s^{- 1} (2 x^{2} - 1) = c o t^{- 1} (\frac{2 x^{2} - 1}{2 x \sqrt{1 - x^{2}}})$ for $x ϵ (0, 1)$

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Similar questions

2 c o s^{- 1} x = c o t^{- 1} (\frac{2 x^{2} - 1}{2 x \sqrt{1 - x^{2}}})

The solution set of the equation $t a n^{- 1} x - c o t^{- 1} x = c o s^{- 1} (2 - x)$ is

2 {cos}^{- 1} x = {cos}^{- 1} (2 x^{2} - 1)

2 {cos}^{- 1} x = {sin}^{- 1} (2 x \sqrt{1 - x^{2}})

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