Is (1+sec(θ))/(sec(θ))=2cos^2(θ/2) ?

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

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prove (1+sec(θ))/(sec(θ))=2cos^2(θ/2)

prove

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

True

Solution steps

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

Let:

u = \frac{θ}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

sin (θ) + cos (θ) = 1

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

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