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2*sin^(-1)(3x-4x^(3))...

2*sin^(-1)(3x-4x^(3))

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Statement I If y=sin^(-1)(3x-4x^(3)), then (dy)/(dx)=(3)/(sqrt(1-x^(2))) only when (-1)/(2)lexlt(1)/(2)/. Statement II sin^(-1)(3x-4x^(3)) ={(-pi-3sin^(-1)x,,-1lexle-(1)/(2),),(3sin^(-1)x,,-(1)/(2)lexle(1)/(2),),(pi-3sin^(-1)x,,(1)/(2)lexle1,):}

Statement I If y=sin^(-1)(3x-4x^(3)), then (dy)/(dx)=(3)/(sqrt(1-x^(2))) only when (-1)/(2)lexlt(1)/(2)/. Statement II sin^(-1)(3x-4x^(3)) ={(-pi-3sin^(-1)x,,-1lexle-(1)/(2),),(3sin^(-1)x,,-(1)/(2)lexle(1)/(2),),(pi-3sin^(-1)x,,(1)/(2)lexle1,):}

Statement I If y=sin^(-1)(3x-4x^(3)), then (dy)/(dx)=(3)/(sqrt(1-x^(2))) only when (-1)/(2)lexlt(1)/(2)/. Statement II sin^(-1)(3x-4x^(3)) ={(-pi-3sin^(-1)x,,-1lexle-(1)/(2),),(3sin^(-1)x,,-(1)/(2)lexle(1)/(2),),(pi-3sin^(-1)x,,(1)/(2)lexle1,):}

Prove the following : 3sin^(-1)x=sin^(-1)(3x-4x^(3)),x epsilon[-1/2, 1/2]