The correct options are
A sec2 x, if x∈(0,π2)
B −sec2 x, if x∈(π2,π)
We have,
y=√1−cos 2x1+cos 2x, x∈(0,π2)∪(π2,π)⇒y=√2 sin2 x2 cos2 x=√tan2 x⇒y=(tan x|, where x∈(0,π2)∪(π2,π)y=⎛⎜⎝tan x, if x∈(0,π2)−tan x, if x∈(π2,π)Differentiating both sides w.r.t. x, we getdydx=⎛⎜⎝sec2 x, if x∈(0,π2)−sec2 x, if x∈(π2,π)