Is cot(1/2 x)=(sin(x))/(1-cos(x)) ?

The answer to whether cot(1/2 x)=(sin(x))/(1-cos(x)) is True

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prove cot(1/2 x)=(sin(x))/(1-cos(x))

prove

cot (\frac{1}{2} x) = \frac{sin ( x )}{1 - cos ( x )}

True

Solution steps

cot (\frac{1}{2} x) = \frac{sin ( x )}{1 - cos ( x )}

Let:

u = \frac{1}{2} x

cot (u) = \frac{sin ( 2 u )}{1 - cos ( 2 u )}

Prove

cot (u) = \frac{sin ( 2 u )}{1 - cos ( 2 u )} :

True

Therefore

cot (\frac{1}{2} x) = \frac{sin ( x )}{1 - cos ( x )}

We showed that the two sides could take the same form

\Rightarrow True

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tan (\frac{4 π}{3} - \frac{π}{4}) = 2 - 3

sec (x) + tan (x) = \frac{1}{( sec ( x ) - tan ( x ) )}

Is cot(1/2 x)=(sin(x))/(1-cos(x)) ?
The answer to whether cot(1/2 x)=(sin(x))/(1-cos(x)) is True