Prove that: `cos^(-1)(x)+cos^(-1)"{"x/2+(sqrt(3-3x^2))/2")"=pi/3`

Find the value of cos^(-1)(x)+cos^(-1)((x)/(2)+(sqrt(3-3x^(2)))/(2))

If (1)/(sqrt2) lt x lt 1 , then prove that cos^(-1) x + cos^(-1) ((x + sqrt(1 - x^(2)))/(sqrt2)) = (pi)/(4)

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

Solve: cos^(- 1)xsqrt(3)+cos^(- 1)x=pi/2

Prove that : cos^(-1) x = 2 cos^(-1) sqrt((1+x)/(2)) (ii) Prove that : tan^(-1)((cosx + sin x)/(cosx - sin x)) = (pi)/(4)+ x

If x lt 0 , then prove that cos^(-1) x = pi - sin^(-1) sqrt(1 - x^(2))

If f(x)=cos^(- 1)x+cos^(- 1){x/2+1/2sqrt(3-3x^2)} then

If x lt 0 , then prove that cos^(-1) x = pi + tan^(-1). (sqrt(1 - x^(2)))/(x)

In function f(x)=cos^(-1)x+cos^(-1)(x/2+(sqrt(3-3x^2))/2) , then Range of f(x) is [pi/3,(10pi)/3]] Range of f(x) is [pi/3,5pi] f(x) is one-one for x in [-1,1/2] f(x) is one-one for x in [1/2,1]

Prove that: "sin"[cot^(-1){"cos"(tan^(-1)x)}]=sqrt((x^2+1)/(x^2+2)) cos [tan^(-1) (cot^(-1)x)}]=sqrt((x^2+1)/(x^2+2))