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

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

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

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

cos(A/2)=+-sqrt((1+cos A)/(2))

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

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

Statement -1: if -1lexle1 then sin^(-1)(-x)=-sin^(-1)x and cos^(-1)(-x)=pi-cos^(-1)x Statement-2: If -1lexlex then cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))= 2cos^(-1)sqrt((1+x)/(2))

If y = cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2) , -1/2ltxlt0 , find (dy)/(dx)

If y=cot^(-1)(sqrt(cos"x"))-tan^(-1)(sqrt(cos"x")), prove that siny=tan^2x/2