sin^(-1)x+tan^(-1)x=pi/2

A : The maximum value of f(x)=Sin^(-1)x+Cos^(-1)x-Tan^(-1)x" is "3pi//4 R : Sin^(-1)x+Cos^(-1)x=pi//2AAx inR

If A = (1)/(pi) [{:(sin^(-1)(pix),, tan^(-1)((x)/(pi))),(sin^(-1)((x)/(pi)),,cot^(-1)((x)/(pi))):}] B = (1)/(pi) [{:(-cos^(-1)(pix),, tan^(-1)((x)/(pi))),(sin^(-1)((x)/(pi)),,-tan^(-1)((x)/(pi))):}] then A - B is equal to

If sin^(-1)x+tan^(-1)((1)/(2))=(pi)/(2) then x=

If A = 1/pi [(sin^(-1)(xpi),tan^(-1)(x/pi)),(sin^(-1)(x/pi),cot^(-1)(pix))] B = 1/pi [(-cos^(-1)(xpi),tan^(-1)(x/pi)),(sin^(-1)(x/pi),-tan^(-1)(pix))] then A-B is equal to :

If A=(1)/(pi)[{:(sin^(-1)(pix),tan^(-1)(x//pi)),(sin^(-1)(x//pi),cot^(-1)(pix)):}] and B=(1)/(pi)[{:(-cos^(-1)(pix),tan^(-1)(x//pi)),(sin^(-1)(pi//x),-tan^(-1)(pix)):}] then find (A-B)

Number of values of x satisfying simultaneously sin^(-1) x = 2 tan^(-1) x " and " tan^(-1) sqrt(x(x-1)) + cosec^(-1) sqrt(1 + x - x^(2)) = pi/2 , is

Number of values of x satisfying simultaneously sin^(-1) x = 2 tan^(-1) x " and " tan^(-1) sqrt(x(x-1)) + cosec^(-1) sqrt(1 + x - x^(2)) = pi/2 , is