Is tan(x/2)=(tan(x))/(sec(x)+1) ?

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

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prove tan(x/2)=(tan(x))/(sec(x)+1)

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

sec^{2} (θ) - 1 = tan^{2} (θ)

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

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