If `y=sqrt((1-cos2x)/(1+cos2x),)x in (0,pi/2)uu(pi/2,pi),` then find `(dy)/(dx)dot`

Explanation

Given,`y=sqrt((1-cos2x)/(1+cos2x)`

=`sqrt((2sin^2x)/(2cos^2x))`

=`sqrt(tan^2x)`

=`|tanx|` where `x in(0,pi/2) uu (pi/2,pi)`


=`{tanx,x in(0,pi/2),}
{-tanx, x in (pi/2,pi)}`
So,`(dy/dx)={sec^2x,x in(0,pi/2),}
{-sec^2x, x in (pi/2,pi)}`