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

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

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

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

tan (x + \frac{π}{4}) = \frac{tan ( x ) + 1}{1 - tan ( x )}

csc (θ) cos (θ) tan (θ) = 1

sin (θ) cos (φ) = \frac{sin ( θ + φ ) + sin ( θ - φ )}{2}

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

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