(4a)cos^(-1)(sqrt((1+x)/(2)))

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

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

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

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))))

Let f(x)=(pi)/(4)+cos^(-1)((x)/(sqrt(1+x^(2))))tan^(-1)x and a_(i)(a_(i)a_(i+1)AA i=1,2,3,......,n) be the positive integral values of x for which sgn(f(x))=1, where sgn(y) denotes signum function ofy.Find sum_(i=1)^(n)a_(i)^(2)

int_(-(1)/(sqrt(3)))^(-(1)/(sqrt(3)))(x^(4))/(1-x^(4))cos^(-1)((2x)/(1+x^(2)))dx

The value of cos^(-1)[cot(sin^(-1)(sqrt((2-sqrt(3))/(4)))+cos^(-1)((sqrt(12))/(4))+sec^(-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)))=

The domain of the function f(x)=4sqrt(cos^(-1)((1-|x|)/(2))) is

The domain of the function f(x)=4sqrt(cos^(-1)((1-|x|)/(2))) is