" 2.(i) "sin^(-1)(-x)=-sin^(-1)x,x in[-1,1]

Prove that sin^(-1)(3x-4x^3)=3sin^(-1)x,x in[1/2,1]

sin^(-1)[sqrt(x^(2)-x^(3))-sqrt(x-x^(3))]=..... a) sin^(-1)x+sin^(-1)sqrt(x) b) sin^(-1)x-sin^(-1)sqrt(x) c) sin^(-1)sqrt(x)-sin^(-1)x d) 2sin^(-1)x

" 4.(i) "int(sin x)/(1-sin^(2)x)dx

Solve the following equations: sin^(-1)((3x)/5)+sin^(-1)((4x)/5)=sin^(-1)x sin^(-1)6x+sin^(-1)6sqrt(3)x=pi/2

Let t_(1)= (sin^(-1)x)^(sin^(-1)x),t_(2)= (sin^(-1) x)^(cos^(-1)x),t_(3) = (cos^(-1)x)^(sin^(-1)x),t_(4) = (cos^(-1)x)^(cos^(-1)x) , Match the follwing items of Column I with Column II

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,):}

sin^(-1)[xsqrt(1-x) - sqrtxsqrt(1-x^2)] (i) sin^(-1)x+sin^(-1)(sqrtx) (ii) sin^(-1)x-sin^(-1)(sqrtx) (iii) sin^(-1)(sqrtx)-sin^(-1)x (iv) None of these

" (2) "sin^(-1)x+sin^(-1)(1/x)+cos^(-1)x+cos^(-1)(1/x)" is equal to "