(1)/(x)+(1)/(sqrt(1-x^(2)))=(35)/(12)

Show that int_(0)^(1//2)(x sin^(-1)x)/(sqrt(1-x^(2)))dx = (1)/(2)-(sqrt(3))/(12)pi

tan^(-1)sqrt((1-x)/(1+x))+sin^(-1)2x sqrt(1-x^(2))=(5 pi)/(12) if x=

(d)/(dx)[cos^(-1)(x sqrt(x)-sqrt((1-x)(1-x^(2))))]=(1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(-1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))+(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))0 b.1/4c.-1/4d none of these

The value of integral int e^(x)((1)/(sqrt(1+x^(2)))+(1)/(sqrt((1+x^(2))^(5))))dx is equal to e^(x)((1)/(sqrt(1+x^(2)))+(1)/(sqrt((1+x^(2))^(3))))+ce^(x)((1)/(sqrt(1+x^(2)))-(1)/(sqrt((1+x^(2))^(5))))+ce^(x)((1)/(sqrt(1+x^(2)))+(1)/(sqrt((1+x^(2))^(5))))+c none of these

If x=(1)/(2)(sqrt(a)+(1)/(sqrt(a))) , then show that (sqrt(x^(2)-1))/(x-sqrt(x^(2)-1))=(a-1)/(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)))=

Prove that : tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))=(pi)/(4)+(1)/(2) cos^(-1)x^(2)

tan^(-1)[(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))]=(pi)/(4)+(1)/(2)cos^(-1)x^(2)

Prove that tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))=(pi)/(4)+(1)/(2) cos^(-1)x^(2) .