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

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

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

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

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

Number of solution of equation Sin^-1((3x)/5)+Sin^-1((4x)/5)=Sin^-1x , x in [-1,1] is

Differentiate tan^(-1)((x-1)/(x+1)) with respect to sin^(-1)(3x-4x^(3)), if -(1)/(2)

lim_(x rarr0)(sin^(-1)x-sin x)/(x^(3)) 1) (1)/(2) , 2) (1)/(3) , 3) (1)/(4) , 4) (1)/(5)

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))

Let cos^(-1)(4x^(3)-3x)=a+b cos^(-1)x Q. If x in [-(1)/(2), (1)/(2)] , then sin^(-1)("sin"(a)/(b)) is :

sin^(-1)(3x -4x^(3)) = lambda sin^(-1)x then lambda =______.