`tan^(2)x = 3"cosec"^(2)x-1`

Solve : 2 tan^(-1) (cos x ) = tan^(-1) (2 "cosec" x)

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

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

Show that 2 tan^-1 x = cosec^-1((1+x^2)/(2x)), 0 < |x| le 1

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

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

sec^(2)(tan^(-1)3)+cosec^(2)(cot^(-1)3) = ____

Solve for x, 2 tan ^(-1)(cos x) =tan^(-1) (2"cosec"x) .

Solve 2 tan^(-1)(cos x) =tan^(-1)(2 "cosec"x) .