Solve: `(-1)/(|x|-2)geq1,w h e r ex in R ,x!=+-2.`

2"tan"(tan^(-1)(x)+tan^(-1)(x^3)),w h e r ex in R-{-1,1}, is equal to

If cot^2x=cot(x-y)(x-z),t h e ncot2x is equal to (w h e r ex!=pi/4)

If f(x)=x/(sinx) \ a n d \ g(x)=x/(tanx),w h e r e \ 0ltxlt=1, then in this interval

Prove that derivative of sec^(-1) (1/(2x^2 - 1)) , x gt 0 , w.r.t. sqrt(1 - x^2) is equal to derivative of log_e x^2 w.r.t.x.

Show that the polynomial x^(4p)+x^(4q+1)+x^(4r+2)+x^(4s+3) is divisible by x^3+x^2+x+1, w h e r ep ,q ,r ,s in ndot

Let a ,b , c ,p ,q be real numbers. Suppose alpha,beta are the roots of the equation x^2+2p x+q=0,alphaa n d1//beta are the roots of the equation a x^2+2b x+c=0,w h e r ebeta^2 !in {-1,0,1}dot Statement 1: (p^2-q)(b^2-a c)geq0 Statement 2: b!=p aorc!=q a

Differentiate tan^(-1)(2x)/(1 - x^2) w.r.t. tan^(-1) x .

int_0^x[cost]dt ,w h e r ex in (2npi,2npi+pi/2),n in N ,a n d[dot] denotes the greatest integer function . then the value of f(1/pi) is

Differentiate cos^(-1) ((1 - x^2)/(1 + x^2)) , 0 lt x lt 1 . w.r.t.x

Differentiate cos^(-1)((1 - x^2)/(1 + x^2)) w.r.t. tan^(-1)x .