`lim_(x->1/sqrt2 ^+) cos^- 1(2xsqrt(1-x^2))/((x-1/sqrt2))-lim_(x->1/sqrt2^-) cos^- 1(2xsqrt(1-x^2))/((x-1/sqrt2))`

lim_(x rarr(1)/(sqrt(2)^(+)))(cos^(-1)(2x sqrt(1-x^(2))))/((x-(1)/(sqrt(2))))-lim_(x rarr(1)/(sqrt(2)^(-)))(cos^(-1)(2x sqrt(1-x^(2))))/((x-(1)/(sqrt(2))))

lim _(x to ((1)/(sqrt2))^(+))(cos ^(-1) (2x sqrt(1- x ^(2))))/((x-(1)/(sqrt2)))- lim _(x to ((1)/(sqrt2))^(-))(cos ^(-1) (2x sqrt(1-x ^(2))))/((x- (1)/(sqrt2)))=

Differentiate each of the following functions with respect to x : (i) sin^(-1)(2xsqrt(1-x^2)),-1/(sqrt(2))ltxlt1/(sqrt(2)) (ii) cos^(-1)(2x(sqrt(1-x^2)),-1/sqrt(2)ltxlt1/sqrt2

y = sin^(-1)(2xsqrt(1 - x^2)), -1/(sqrt2) lt x lt 1/(sqrt2)

int(1)/(cos^(-1)x.sqrt(1-x^(2)))dx=

int(1)/(cos^(-1)x.sqrt(1-x^(2)))dx=

Show that (i) sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,-1/(sqrt(2))lexle1/(sqrt(2)) (ii) sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1)x,1/(sqrt(2))lexle1

Show that (i) sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,-1/(sqrt(2))lexle1/(sqrt(2)) (ii) sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1)x,1/(sqrt(2))lexle1