`y=cos^(-1)(sqrt((1-cos(x^(2)))/(2)))`

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

f(x)=cos^(-1)(x^(2)/sqrt(1+x^(2)))

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

If y=cos^(-1){(2x-3sqrt(1-x^2))/(sqrt(13))},"f i n d"(dy)/(dx)

Evaluate the following limit: (lim)_(x->1/(sqrt(2)))(cos^(-1)(2xsqrt(1-x^2)))/(x-1/(sqrt(2)))

Write the simplest form : cos^(-1)(sqrt(((sqrt(1+x^2) +1)/(2sqrt(1+x^2))))

sin^(- 1)x+sin^(- 1)y=cos^(- 1) (sqrt(1-x^2) sqrt(1-y^2)-xy) if x in [0,1], y in [0,1]

If y = cos^(-1) ((1)/( sqrt(1+t^(2)))), x = sin^(-1) (sqrt((t^(2))/(1 + t^(2)))), "find " (dy)/(dx)

Evaluate lim_(ntooo) n^(2){sqrt((1-"cos"(1)/(n))sqrt((1-"cos"(1)/(n))sqrt((1-"cos"(1)/(n))...)))} .

If y=cos^(-1)((3x+4\ sqrt(1-x^2))/5) , find (dy)/(dx)