Is cos(a)=2cos^2(a/2)-1 ?

The answer to whether cos(a)=2cos^2(a/2)-1 is True

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prove cos(a)=2cos^2(a/2)-1

prove

cos (a) = 2 cos^{2} (\frac{a}{2}) - 1

True

Solution steps

cos (a) = 2 cos^{2} (\frac{a}{2}) - 1

Let:

u = \frac{a}{2}

cos (2 u) = 2 cos^{2} (u) - 1

Prove

cos (2 u) = 2 cos^{2} (u) - 1 :

True

Therefore

cos (a) = 2 cos^{2} (\frac{a}{2}) - 1

We showed that the two sides could take the same form

\Rightarrow True

tan^{3} (x) = \frac{sin ^{3} ( x )}{cos ^{3} ( x )}

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

tan^{2} (x) - sin^{2} (x) = (tan (x) sin (x))^{2}

cos^{2} (θ) = sin^{2} (θ) - 1

\frac{sec ( θ )}{sec ( θ ) - 1} = \frac{1}{1 - cos ( θ )}