`(xtendsto0)(cos^(2)x-sin^(2)x-1)/(sqrt(x^(2)+1)-1)`

If f(x) is continuous at x=0 , where f(x)={:{((cos^(2)x-sin^(2)x-1)/(sqrt(x^(2)+1)-1)", for " x!=0),(2k", for " x=0):} , then k=

if f(x)=(cos^(2)x-sin^(2)x-1)/(sqrt(x^(2)+1)-1),x!=0 and f(x)=k,x=0 is continuous at x=0 then k=

3cos^(-1)x=sin^(-1)(sqrt(1-x^(2))(4x^(2)-1))

sin^(-1)x=cos^(-1)sqrt(1-x^(2))

Solve 2cos^(-1)x=sin^(-1)(2x sqrt(1-x^(2)))

2sin^(2)x+sqrt(3)cos x+1=0

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

Solve 2 cos^(-1) x = sin^(-1) (2 x sqrt(1 - x^(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))

The value of (lim_(x rarr0)((cos x-sqrt(1+sin^(2)x))/(1-sqrt(1+tan^(2)x)))) is equal to "