Solve the equation: `tan^(-1)sqrt(x^2+x)+sin^(-1)sqrt(x^2+x+1)=pi/2`

The number of real roots of the equation tan^(-1)sqrt(x(x+1))+sin^(-1)sqrt(x^(2)+x+1)=(pi)/(4) is :

The sum of solutions of the equation 2 sin^(-1) sqrt(x^(2)+x+1)+cos^(-1) sqrt(x^(2)+x)=(3pi)/(2) is :

The number of solutions for the equation sin^(-1) sqrt((x^(2)-x+1))+cos^(-1)sqrt((x^(2)-x))=pi is :

Solve the equation sin^(-1)6x+sin^(-1)6sqrt(3)x=(-pi)/(2)

The number of solutions for the equation 2 sin^(-1)(sqrt(x^(2) - x + 1)) + cos^(-1)(sqrt(x^(2) - x) )= (3pi)/(2) is