Solution:∫sin-1 x-cos-1 xsin-1 x+cos-1 x dxsin-1 x+cos-1 x=π2=2π∫sin-1 x-cos-1 x dx=2π∫sin-1 x dx-∫cos-1 x dx=2πx sin-1 x+1-x2-x cos-1 x+1-x2+C=2πx sin-1 x-x cos-1 x+21-x2+Ca ∫sin-1 x dx=x sin-1 x+1-x2b ∫cos-1 x dx=x cos-1 x-1-x2

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Solution : \int \frac{\sin^{- 1} x - \cos^{- 1} x}{\sin^{- 1} x + \cos^{- 1} x} dx \sin^{- 1} x + \cos^{- 1} x = \frac{π}{2} = \frac{2}{π} \int (\sin^{- 1} x - \cos^{- 1} x) dx = \frac{2}{π} (\int \sin^{- 1} x dx - \int \cos^{- 1} x dx) = \frac{2}{π} (x \sin^{- 1} x + \sqrt{1 - x^{2}} - x \cos^{- 1} x + \sqrt{1 - x^{2}}) + C = \frac{2}{π} (x \sin^{- 1} x - x \cos^{- 1} x + 2 \sqrt{1 - x^{2}}) + C a . \int \sin^{- 1} x dx = x \sin^{- 1} x + \sqrt{1 - x^{2}} b . \int \cos^{- 1} x dx = x \cos^{- 1} x - \sqrt{1 - x^{2}}

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