`intcot^(-1)sqrt((1+cos2x)/(1-cos2x))dx` is:

Explanation

We have
`y=sqrt((1-cso2x)/(1+cos2x)),=sqrt((2sin^(2)x)/(2cos^(2)x))=sqrt(tan^(2)x)`
`=|tanx|," where "x in(0,(pi)/(2))cup((pi)/(2),pi)`
`={{:(tan x, x in(0,(pi)/(2)),),(-tan x, x in((pi)/(2),pi),):}`
`therefore" "(dy)/(dx)={{:(sec^(2)x",", x in(0,(pi)/(2)),),(-sec^(2) x",", x in((pi)/(2),pi),):}`