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

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

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

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

cos (u) (1 - cos (2 u)) = sin (u) sin (2 u)

Prove

cos (u) (1 - cos (2 u)) = sin (u) sin (2 u) :

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{csc ( x ) - cot ( x )}{sec ( x ) - 1} = csc (x)

\frac{csc ^{2} ( t )}{cot ( t )} = tan (t) + cot (t)

\frac{2}{sin ( θ )} = 2 csc (θ)

cos (x) (1 - sin^{2} (x)) = cos^{3} (x)

4 (5 cos (2 x)) + (- 20 cos (2 x)) = 0

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