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

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

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

If f(x)=cos^(-1)(4x^(3)-3x), x in [-1,1] , then

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

Prove that cos^(-1){(1+x)/(2)}=(cos^(-1)x)/(2)

Prove that cos^(-1)x+cos^(-1) [x/2 +(sqrt(3-3x^(2)))/2 ] = pi/3 , 1/2 le x le 1

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 If x in[-(1)/(2),-1], then a+b pi=

co sec^(-1)((1)/(3x-4x^(3)))

prove that cot^(-1)[sqrt((1+cos3x)/(1-cos3x))]