Is csc^2(x/2)=(2sec(x))/(sec(x)-1) ?

The answer to whether csc^2(x/2)=(2sec(x))/(sec(x)-1) is True

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prove csc^2(x/2)=(2sec(x))/(sec(x)-1)

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

csc^{2} (u) = \frac{2 sec ( 2 u )}{sec ( 2 u ) - 1}

Prove

csc^{2} (u) = \frac{2 sec ( 2 u )}{sec ( 2 u ) - 1} :

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{sec ( x )}{- csc ( x )} + \frac{- sin ( x )}{cos ( x )} = - 2 tan (x)

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

\frac{sin ^{2} ( x )}{1} \cdot \frac{1}{sin ^{2} ( x )} = 1

\frac{1}{2} cot (x) - \frac{1}{2} tan (x) = cot (2 x)

cos^{2} (2 x) - sin^{2} (2 x) = 0

Is csc^2(x/2)=(2sec(x))/(sec(x)-1) ?
The answer to whether csc^2(x/2)=(2sec(x))/(sec(x)-1) is True