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

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

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

prove

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

True

Solution steps

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

Let:

u = \frac{t}{2}

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

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{1}{2} sec (x) - 1 = 0

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

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

cot^{2} (x) sec^{2} (x) = 1 + \frac{1}{tan ^{2} ( x )}

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