We'll apply double angle identity for sin 2x and cos
2x:
sin 2x = 2sin x*cos
x
1+cos 2x = 1 - 1 + 2(cos
x)^2
1+cos 2x = 2(cos
x)^2
We'll re-write the
fraction:
sin 2x/(1+cos 2x) = 2sin x*cos x/2(cos
x)^2
We'll divide both numerator and denominator by 2 cos
x:
sin 2x/(1+cos 2x) = sin x/cos
x
sin 2x/(1+cos 2x) = tan
x
The fraction written as a function of x is: sin 2x/(1+cos
2x) = tan x.
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