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

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

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

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

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