If ∫sin⁡−1xcos⁡−1x dx=f−1(x) [Ax−xf−1(x)−21−x2]+π21−x2+2x+C\int \sin^{-1}x\cos^{-1}x\,dx=f^{-1}(x)\,[Ax-xf^{-1}(x)-2\sqrt{1-x^2}]+\frac{\pi}{2}\sqrt{1-x^2}+2x+C…

Mathematics

Problem

If ∫sin⁡−1xcos⁡−1x dx=f−1(x) [Ax−xf−1(x)−21−x2]+π21−x2+2x+C\int \sin^{-1}x\cos^{-1}x\,dx=f^{-1}(x)\,[Ax-xf^{-1}(x)-2\sqrt{1-x^2}]+\frac{\pi}{2}\sqrt{1-x^2}+2x+C then (a) f(x)=sin⁡xf(x)=\sin x (b) f(x)=cos⁡xf(x)=\cos x (c) A=π4A=\frac{\pi}{4} (d) A=π2A=\frac{\pi}{2} (a) f(x)=sin⁡xf(x)=\sin x (b) f(x)=cos⁡xf(x)=\cos x (c) A=π4A=\frac{\pi}{4} (d) A=π2A=\frac{\pi}{2}

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