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

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

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

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

cos (4 θ) = 8 cos^{4} (θ) - 8 cos^{2} (θ) + 1

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

sin (2 A) = 2 sin (A) cos (A)

tan (A - B) = sin (A - B) sec (A - B)

cot^{2} (θ) (1 - cos^{2} (θ)) = cos^{2} (θ)

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