The problem here is "how far back do we need to go?" when we try to explain "why?"
Assuming that the following identities are known:
sin^2(x)+cos^2(x) = 1sin2(x)+cos2(x)=1
and
sin(2x) = 2sin(x)cos(x)sin(2x)=2sin(x)cos(x)
(sin(x))/(cos(x)) + (cos(x))/(sin(x))sin(x)cos(x)+cos(x)sin(x)
= (sin(x))/(cos(x)) * (sin(x))/(sin(x)) + (cos(x))/(sin(x)) * (cos(x))/(cos(x))=sin(x)cos(x)⋅sin(x)sin(x)+cos(x)sin(x)⋅cos(x)cos(x)
= (sin^2(x)+cos^2(x))/cos(x)sin(x)=sin2(x)+cos2(x)cos(x)sin(x)
= 1/(cos(x)sin(x))=1cos(x)sin(x)
or
= 2/sin(2x)=2sin(2x)
