prove that `tan^(-1)x+cot^(-1)x=pi/2`

3tan^(-1)x+cot^(-1)x=pi

Prove that tan^(-1) x + cot^(-1) (x+1) = tan ^(-1) (x^(2) + x+1) .

Prove that cos tan^(-1)sin cot^(-1)x=sqrt((x^(2)+1)/(x^(2)+2))

Prove that : tan^(-1) x + cot^(-1) (1+x) = tan^(-1) (1+x+x^2)

Prove that : tan^(-1) x+cot^(-1) y = tan^(-1) ((xy+1)/(y-x))

Prove that tan^(-1)(cot x)+cot^(-1)(tan x)=pi-2x

Prove that : (i) tan^(-1) x + cot^(-1)( x+1) = tan^(-1) (x^(2)+x+1) (ii) cot^(-1) 3 + "cosec"^(-1) sqrt(5) = pi/4

Prove that 2 tan^(-1) (cosec tan^(-1) x - tan cot^(-1) x) = tan^(-1) x (x != 0)

Prove that tan^(-1) x + tan ^(-1). 1/x = {{:(pi//2", if " x gt 0),(-pi//2", if "x lt 0 ):} .

Prove that tan^(-1) x + tan^(-1).(1)/(x) = {(pi//2,"if" x gt 0),(-pi//2," if " x lt 0):}