18*(x cos^(-1)x)/(sqrt(1-x^(2)))

If y=(x cos^(-1)x)/(sqrt(1-x^(2)))-log sqrt(1-x^(2)), then prove that (dy)/(dx)=(co^(1-x)x)/((1-x^(2))^((3)/(2)))

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

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

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)))=

If 1/(sqrt(2))

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

If x takes negative permissible values , then sin^(-1) x= a) cos^(-1)sqrt(1-x^2) b) -cos^(-1)sqrt(1-x^2) c) cos^(-1)sqrt(x^2-1) d) pi-cos^(-1)sqrt(1-x^2)

cos^(-1)((x^(2))/(6)+sqrt(1-(x^(2))/(9))sqrt(1-(x^(2))/(4)))=cos^(-1)((x)/(3))-cos^(-1)((x)/(2)) hold for all x belonging to