Is 4sin(x/4)cos(x/4)cos(x/2)=sin(x) ?

The answer to whether 4sin(x/4)cos(x/4)cos(x/2)=sin(x) is True

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prove 4sin(x/4)cos(x/4)cos(x/2)=sin(x)

prove

4 sin (\frac{x}{4}) cos (\frac{x}{4}) cos (\frac{x}{2}) = sin (x)

True

Solution steps

4 sin (\frac{x}{4}) cos (\frac{x}{4}) cos (\frac{x}{2}) = sin (x)

Let:

u = \frac{x}{4}

4 sin (u) cos (u) cos (2 u) = sin (4 u)

Prove

4 sin (u) cos (u) cos (2 u) = sin (4 u) :

True

Therefore

4 sin (\frac{x}{4}) cos (\frac{x}{4}) cos (\frac{x}{2}) = sin (x)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{sin ( θ ) + sin ( 3 θ )}{2 sin ( 2 θ )} = cos (θ)

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

cos (b) csc (b) tan (b) = 1

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

Is 4sin(x/4)cos(x/4)cos(x/2)=sin(x) ?
The answer to whether 4sin(x/4)cos(x/4)cos(x/2)=sin(x) is True