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

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

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

prove

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

True

Solution steps

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

Let:

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

We showed that the two sides could take the same form

\Rightarrow True

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sin^{2} (x) sec (x) csc (x) = tan (x)

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

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