Is cos(a/2)=sqrt((1+cos(a))/2) ?

The answer to whether cos(a/2)=sqrt((1+cos(a))/2) is True

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prove cos(a/2)=sqrt((1+cos(a))/2)

prove

cos (\frac{a}{2}) = \frac{1 + cos ( a )}{2}

True

Solution steps

cos (\frac{a}{2}) = \frac{1 + cos ( a )}{2}

Let:

u = \frac{a}{2}

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

Prove

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

False

Therefore

cos (\frac{a}{2}) = \frac{1 + cos ( a )}{2}

We showed that the two sides could take the same form

\Rightarrow True

sin (β) = \frac{1}{2}

cos^{4} (θ) = \frac{1}{4} + \frac{cos ( 2 θ )}{2} + \frac{cos ^{2} ( 2 θ )}{4}

sin (x) (tan^{2} (x) + 1) = tan (x) sec (x)

csc (u) = 2

\frac{csc ( x )}{cot ( x )} = csc (x) tan (x)

Is cos(a/2)=sqrt((1+cos(a))/2) ?
The answer to whether cos(a/2)=sqrt((1+cos(a))/2) is True