Saturday, June 1, 2013

Write the fraction as a function of x: sin 2x/(1+cos 2x)

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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