For each real `x, -1 lt x lt 1`. Let A(x) be the matrix `(1-x)^(-1) [(1,-x),(-x,1)]` and `z=(x+y)/(1+xy)`. Then

If -1lt x lt 0 then tan^(-1) x equals

If -1 lt x lt 0 , then cos^(-1) x is equal to

Solve the inequation (x^(2)+x+1)^(x)lt1

If 0 lt x lt 1 then tan^(-1) (2x)/(1-x^(2)) equals

For |x| lt 1/5 , the coefficient of x^(3) in the expansion of (1)/((1-5x)(1-4x)) is

If y=log((1-x^(2))/(1+x^(2))),|x|lt1 , then (dy)/(dx) =

If x lt 0 , lt 0 , x + y +(x)/4=(1)/(2) and (x+y)((x)/y)=-(1)/(2) then :

Let x_(1) , x_(2) , x_(3) be the solution of tan^(-1) ((2x + 1)/(x +1 )) + tan ^(-1) ((2x - 1)/( x -1 )) = 2 tan ^(-1) ( x + 1) " where " x_(1) lt x_(2) lt x_(3) " , then " 2x_(1) + x_(2) + x_(3)^(2) is equal to

If y=e^(asin^(-1)x)\ ,\ -1\ lt=x\ lt=1, then show that (1-x^2)\ (d^2\ y)/(dx^2)-\ x(dy)/(dx)-\ a^2y=0

Prove that : |{:(1,x,yz),(1,y,zx),(1,z,xy):}|=(x-y)(y-z)(z-x)