(ii)sin^(-1)(4x^(3)-3x)

3sec^(-1)(1/x)-sin^(-1)(4x^(3)-3x)=

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

If y=sin ^(-1) (4x^(3) -3x) ,then ( dy)/(dx) =

Prove that: i) sin^(-1)(3x-4x^(3))=3sin^(-1)x, |x| le 1/2 ii) cos^(-1)(4x^(2)-3x)=3cos^(-1)x,1/2 le x le 1 iii) tan^(-1)""(3x-x^(3))/(1-3x^(2))=3tan^(-1)x, |x| lt 1/sqrt(3) iv) tan^(-1)x+tan^(-1)""(2x)/(1-x^(2))=tan^(-1)""(3x-x^(3))/(1-3x^(2))

Find (d)/(dx)sin^(-1)(3x-4x^(3))=

int(sin^(-1)(3x-4x^(3))dx)

int(sin^(-1)(3x-4x^3)dx)

Let the solution set of the inequation n(sin x-(1)/(2))(sin x-(1)/(sqrt(2)))<=0in[(pi)/(2),pi] be A and let solution set of equation sin^(-1)(3x-4x^(3))=3sin^(-1)x be B. Now define a function f:A rarr B.

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