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

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to express sin 2x/(1 + cos 2x) in terms of x

sin 2x/(1 + cos 2x)

=> 2*sin x*cos x/(1 + 2*(cos x)^2 - 1)

=> 2*sin x*cos x/2*(cos x)^2

=> sin x*cos x/(cos x)^2

=> sin x/cos x

=> tan x

As a function of x, sin 2x/(1 + cos 2x) = tan x

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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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