sincot-12x1-x3+cos-11-x21+x2=

x=tan A sincot-12tan A1-tan2A+cos-11-tan2A1+tan2A sincot-1tan2A+cos-1cos2A sincot-1cot π2-2A+2A =sinπ2-2A+2A =1

sincot-12x1-x3+cos-11-x21+x2=

x=tan A sincot-12tan A1-tan2A+cos-11-tan2A1+tan2A sincot-1tan2A+cos-1cos2A sincot-1cot π2-2A+2A =sinπ2-2A+2A =1

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$\sin [\cot^{- 1} (\frac{2 x}{1 - x^{3}}) + \cos^{- 1} (\frac{1 - x^{2}}{1 + x^{2}})] =$

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$\frac{x - y}{1 + xy}$

$\frac{2 x}{1 - x^{2}}$

answer is B.

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Detailed Solution

$x = \tan A \sin [\cot^{- 1} (\frac{2 \tan A}{1 - \tan^{2} A}) + \cos^{- 1} (\frac{1 - \tan^{2} A}{1 + \tan^{2} A})] \sin [\cot^{- 1} (\tan 2 A) + \cos^{- 1} (\cos 2 A)] \sin [\cot^{- 1} (\cot (\frac{π}{2} - 2 A)) + 2 A] = \sin (\frac{π}{2} - 2 A + 2 A) = 1$