The given trigonometric identity has been proven as shown below
Trigonometric identities
From the question, we are to complete the proof
Proving the identity
[tex]\frac{1 - cos(2x)}{sin(2x)} = tan(x)[/tex]
The identity can proven as shown
[tex]\frac{1 - cos(2x)}{sin(2x)} = \frac{1-(1-2sin^{2}(x)) }{2sin(x).cos(x)}[/tex]
Clearing the bracket, we get
[tex]\frac{1 - cos(2x)}{sin(2x)} = \frac{1-1+2sin^{2}(x) }{2sin(x).cos(x)}[/tex]
Simplifying
[tex]= \frac{2(sin(x))^{2} }{2sin(x).cos(x)}[/tex]
This can be written as
[tex]= \frac{2(sin(x))(sin(x)) }{2sin(x).cos(x)}[/tex]
Then, we get
[tex]= \frac{sin(x) }{cos(x)}[/tex]
[tex]= tan(x)[/tex]
Hence, the given identity has been proven as shown above.
Learn more on Trigonometric identities here: https://brainly.com/question/7331447
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