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

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

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

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{csc ( x )}{cos ( x )} = tan (x) + cot (x)

\frac{1 + cos ( 2 θ )}{sin ( 2 θ )} = cot (θ)

cot (x) \cdot sin (x) = cos (x)

\frac{sec ( t )}{cos ( t )} - \frac{tan ( t )}{cot ( t )} = 1

\frac{cot ( y )}{sec ( y )} = csc (y) - sin (y)

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