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

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(0,1)

(−1,1)−{0}

(-1,0)

[-1,1]

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detailed solution

Correct option is A

2cos−1x=cot−12x2−12x1−x2Putx=cosθ ; L.H.S. = 2θ where 0≤θ≤πand −1≤x≤1 ……… (1)R.H.S. = cot−1cos2θ2cosθ|sinθ|=cot−1(cot2θ)=2θ if 0<2θ<π …………. (2) From (1) and (2), we get 0<θ<π/2 ∴x∈(0,1)

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Which of the following is the solution set of the equation 2cos−1x=cot−12x2−12x1−x2?

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