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

Solve tan^(-1) x + cot^(-1) (-|x|) = 2 tan^(-1) 6x

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

Prove that : sin cot^(-1) tan cos^(-1) x=x

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

Prove that tan(cot^(-1)x)=cot(tan^(-1)x)

Prove that tan (2 tan^(-1) x ) = 2 tan (tan^(-1) x + tan^(-1) x^(3)) .

Prove that sin cot^(-1) tan cos^(-1) x = sin cosec^(-1) cot tan^(-1) x = x, " where " x in [0,1]

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

The value of 2tan^(-1)(cos ec tan^(-1)x-tan cot^(-1)x) is equal to (a)cot ^(-1)x( b ) (cot^(-1)1)/(x) (c)tan ^(-1)x (d) none of these