Is cos(θ)=2cos^2(θ/2)-1 ?

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

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prove cos(θ)=2cos^2(θ/2)-1

prove

cos (θ) = 2 cos^{2} (\frac{θ}{2}) - 1

True

Solution steps

cos (θ) = 2 cos^{2} (\frac{θ}{2}) - 1

Let:

u = \frac{θ}{2}

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

Prove

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

True

Therefore

cos (θ) = 2 cos^{2} (\frac{θ}{2}) - 1

We showed that the two sides could take the same form

\Rightarrow True

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

cos (4 x) = 1 - 8 cos^{2} (x) + 8 cos^{4} (x)

cot (x) + tan (x) = \frac{1}{sin ( x ) cos ( x )}

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

\frac{csc ( θ ) + sec ( θ )}{tan ( + 1 )} = csc (θ)