Simplify `sincot^(-1)tancos^(-1)x , x >0`

Simplify sin(cot^(-1)(cos(tan^(-1)x))),0 ltxlt1 .

Simplify: x - (3 - x)

Simplify : cot^(-1) ((1)/(sqrt(x^(2) -1))) for x lt -1

Let alpha = tan^-1 (1/2)+tan^-1(1/3) , beta=cos^-1(2/3)+cos^-1(sqrt5/3) , gamma=sin^-1(sin((2pi)/3))+1/2cos^-1(cos((2pi)/3)) then sincot^-1 tancos^-1 (sin gamma) is equal to (A) 2singamma (B) sin(gamma/2) (C) 1/2 sin gamma (D) cosgamma

Column I, Column II (a)sin^(-1)x+x >0, (p) x 0, (q) x in [0,1] (c)tan^(-1)x+x >0, (r) x in [-1,0] (d)cot^(-1)x+x >0, (s) x >0

Solve for x :tan^(-1)((1-x)/(1+x))=1/2tan^(-1)x ,x >0

Simplify the expression 8(x^(2)-x-1) + 5 (2x-2) - 3 (x^(2) +x - 1)

Simplify: x^2(x^2+1)-x^3(x+1)-x(x^3-x)

Simplify: {(1/2)^(-1)x\ (-4)^(-1)}^(-1)