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

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

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

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

cos (\frac{π}{4} - x) + cos (\frac{π}{4} + x) = 2 cos (x)

sin^{4} (x) - cos^{4} (x) = - cos (2 x)

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

\frac{cos ( x )}{tan ( x )} = csc (x) - sin (x)

sec^{2} (θ) csc^{2} (θ) = sec^{2} (θ) + csc^{2} (θ)

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