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

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

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

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

sec (u) = \frac{1}{cos ( u )}

Prove

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

True

sec (u) = \frac{1}{cos ( u )}

Use the basic trigonometric identity:

sec (x) = \frac{1}{cos ( x )}

\Rightarrow True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

1 - sin (x) = cot (x)

4 cos^{2} (θ) + 4 sin^{2} (θ) = 4

\frac{- cos ^{2} ( 2 θ )}{2} = \frac{- 1 - cos ( 4 θ )}{8}

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

2 sin (y) cos (y) sec (2 y) = tan (2 y)

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