Find the domain of `f(x)=cos^-1(sqrt(x^2-x+1))/(sqrt(sin^-1((2x-1)/2))` is the integral `(alpha,beta]` then `alpha+beta`

If the domain of the function f(x) = (cos^(-1)sqrt(x^(2) - x + 1))/(sqrt(sin^(-1)((2x-1)/(2)))) is the interval (alpha, beta] , then alpha + beta is equal to :

find the domain and range of f(x)=sqrt(cos(sin x))+sin^(-1)((1+x^(2))/(2x))

Let coefficient of x^4 and x^2 in the expansion of (x+sqrt(x^2-1))^6+(x-sqrt(x^2-1))^6 is alpha and beta then alpha-beta is equal to

F(x)=x^(5)+log,(x+sqrt(1+x^(2))) , Then for all alpha, beta in R such that alpha+beta gt 0

int_( to )(x^(2)-1)/(x sqrt(x^(2)+alpha x+1)sqrt(x^(2)+beta x+1))dx is equal

if int (1)/(sqrt(9-16x^(2)))dx=alpha sin ^(-1) (beta x) +c. then alpha +(1)/(beta )=

If alpha=sin^(-1)(cos(sin^(-1)x)) and beta=cos^(-1)(sin(cos^(-1)x)) then find tan alpha.tan beta

If lim_(x rarr0)(e^(alpha x^(2))-cos sqrt(beta)x)/(x^(2))=(1)/(2) [ where alpha in R-{0},beta in(0,oo)], then 2 alpha+beta equals

If alpha = sin^(-1) (cos(sin^-1) x)) and beta = cos^(-1) (sin (cos^(-1) x)) , then find tan alpha. tan beta.