`cosec^(-1)((1+tan ^2x)/(2tanx))`

"cosec"^(-1)((1+tan^(2)x)/(2tanx))

Evaluate int[cos^-1((1-tan^2x)/(1+tan^2x))+sin^-1((2tanx)/(1+tan^2x))]dx.

int sin^(-1)((2tanx )/(1+tan^(2)x))dx = ?

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

inttan^(-1)((2tanx)/(1-tan^(2)x))dx=

int((1+sqrt(tanx))(1+tan^(2)x))/(2tanx)dx equals to

int((1+sqrt(tanx))(1+tan^(2)x))/(2tanx)dx equals to

int (tanx sec^(2)x)/((1-tan^(2)x))dx.

"If "y=(tanx)^(cotx)+(cotx)^(tanx)",prove that "(dy)/(dx)=(tanx)^(cotx)."cosec"^(2)x(1-logtanx)+(cotx)^(tanx).sec^(2)x[log(cotx)-1].

Let f(x) = sin (sin^-1 2x) + cosec (cosec^-1 2x) + tan(tan^-1 2x) , then which one of the following statements is/are incorrect ?