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

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

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

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

(sin (x)) (csc (x)) = 1

sin (α) = \frac{2 tan ( \frac{α}{2} )}{1 + tan ^{2} ( \frac{α}{2} )}

(1 + sin (x)) (1 - sin (x)) = \frac{1}{sec ^{2} ( x )}

sin (3 x) cos (2 x) - cos (3 x) sin (2 x) = sin (x)

4 cot^{2} (y) (sec^{2} (y) - 1) = 4

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