2 sin-1x+sin-12x1-x2+3 cos-1x-cos-14x3-3x

=2 sin-1x+sin-12x1-x2+3 cos-1x-cos-14x3-3x ; x∈-1,-12 =2sin-1x+π-2sin-1x+3cos-1-2π-3cos-1x =-π

2 sin-1x+sin-12x1-x2+3 cos-1x-cos-14x3-3x

=2 sin-1x+sin-12x1-x2+3 cos-1x-cos-14x3-3x ; x∈-1,-12 =2sin-1x+π-2sin-1x+3cos-1-2π-3cos-1x =-π

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$2 \sin^{- 1} x + \sin^{- 1} (2 x \sqrt{1 - x^{2}}) + 3 \cos^{- 1} x - \cos^{- 1} (4 x^{3} - 3 x)$

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$- π, when x \in [- 1, \frac{1}{\sqrt{2}}]$

$4 \sin^{- 1} x, when x \in [- 1, 1]$

$- π, when x \in [\frac{- 1}{2}, \frac{1}{2}]$

$4 \sin^{- 1} x + 2 \cos^{- 1} (4 x^{3} - 3 x), x \in [\frac{1}{\sqrt{2}}, 1]$

answer is B.

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$= 2 \sin^{- 1} x + \sin^{- 1} (2 x \sqrt{1 - x^{2}}) + 3 \cos^{- 1} x - \cos^{- 1} (4 x^{3} - 3 x); x \in [- 1, - \frac{1}{\sqrt{2}}] = 2 \sin^{- 1} x + π - 2 \sin^{- 1} x + 3 \cos^{- 1} - 2 π - 3 \cos^{- 1} x = - π$

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2 sin-1x+sin-12x1-x2+3 cos-1x-cos-14x3-3x

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$2 \sin^{- 1} x + \sin^{- 1} (2 x \sqrt{1 - x^{2}}) + 3 \cos^{- 1} x - \cos^{- 1} (4 x^{3} - 3 x)$