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

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

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

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

cos (4 x) = 1 - 2 sin^{2} (2 x)

cos (π - x) + sin (\frac{π}{2} + x) = 0

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

arcsin (x) = csc (x)

\frac{1}{tan ( x ) csc ( x ) sin ( x )} = cot (x)

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