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

6 cos^{2} (x) - 6 sin^{2} (x) = 12 cos^{2} (x) - 6

sin (θ) cot (θ) sec (θ) = 1

cos (2 θ) = \frac{1 - tan ^{2} ( θ )}{1 + tan ^{2} ( θ )}

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

tan (8 θ) - tan (8 θ) tan^{2} (4 θ) = 2 tan (4 θ)

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