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

\frac{1}{tan ( b )} + tan (b) = sec (b) csc (b)

csc^{2} (x) cot^{2} (x) + csc^{2} (x) = csc^{4} (x)

sin^{5} (x) = (sin (x))^{5}

2 tan (x) sec (x) csc (x) = 2 + 2 tan^{2} (x)

\frac{csc ^{2} ( x )}{cot ^{2} ( x )} = csc (x) sec (x)

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