the ascending order of minimum values of the functions `P:sin^(-1)x-cos^(-1)x` `Q:tan^(-1)x+cot^(-1)x` `R:sec^(-1)x-cosec^(-1)x`

Th ascending order of minimum values of functions P: sin^(-1)x-cos^(-1)x Q:tan^(-1)x+cot^(-1)x R:sec^(-1)x-cosec^(-1)x is

sin(sec^(-1)x+"cosec"^(-1)x)

The number of rational numbers in the domain of function y=sin^(-1)x+cos^(-1)x+tan^(-1)x+"cosec"^(-1)x+sec^(-1)x+cot^(-1)x , is ___________ .

The number of rational numbers in the domain of function y=sin^(-1)x+cos^(-1)x+tan^(-1)x+"cosec"^(-1)x+sec^(-1)x+cot^(-1)x , is ___________ .

The sum of the maximum and minimum values of the function f(x)=sin^(-1)4x+cos^(-1)4x+sec^(-1)4x is

If x_1,x_2,x_3,x_4,x_5,x_6 all are independent then the maximum and minimum values of [sin^(-1)x_1]+[cos^(-1)x_2]+[tan^(-1)x_3]+[cot^(-1)x_4]+[sec^(-1)x_5]+[cosec^(-1)x_6] , where [] represents greatest integer function, respectively are

If x_1,x_2,x_3,x_4,x_5,x_6 all are independent then the maximum and minimum values of [sin^(-1)x_1]+[cos^(-1)x_2]+[tan^(-1)x_3]+[cot^(-1)x_4]+[sec^(-1)x_5]+[cosec^(-1)x_6] , where [] represents greatest integer function, respectively are

cos(sec^(-1)x+cosec^(-1)x),|x|ge1

The domain and range of f(x)=sin^(1)x+cos^(-1)x+tan^(-1)x+cot^(-1)x+sec^(-1)x+cos ec^(-1)x respectively are

The maximum and minimum values of f(x)=sin^(-1)x+cos^(-1)x+tan^(-1)x respectively is