Is cos^2(x/2)=(sec(x)+1)/(2sec(x)) ?

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

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prove cos^2(x/2)=(sec(x)+1)/(2sec(x))

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

1 + tan^{2} (y) = sec^{2} (y)

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1 - (sin (x) + cos (x))^{2} = - sin (2 x)

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

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