Is 1-cos(x)=2sin^2(x/2) ?

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

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prove 1-cos(x)=2sin^2(x/2)

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

cos (3 A) = 4 cos^{3} (A) - 3 cos (A)

sin (a) cot (a) = cos (a)

cos (3 θ) = cos^{3} (θ) - 3 sin^{2} (θ) cos (θ)

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

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