Question

How do you simplify `(1+sin2x+cos2x)/(1+sin2x-cos2x)`?

Answer 1

`(1+sin2x+cos2x)/(1+sin2x-cos2x)`

`=(1+2sinxcosx+2cos^2x-1)/(1+2sinxcosx-1+2sin^2x)`

`=(2sinxcosx+2cos^2x)/(2sinxcosx+2sin^2x)`

`=(2cosx(sinx+cosx))/(2sinx(cosx+sinx)`

`=cotx`