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

The answer to whether 4*sin(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 \cdot sin (\frac{x}{4}) \cdot 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

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

Manipulating left side

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

Rewrite using trig identities

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

= 2 \cdot 2 sin (u) cos (u) cos (2 u)

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

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

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

= sin (2 \cdot 2 u)

Simplify

= sin (4 u)

= sin (4 u)

We showed that the two sides could take the same form

\Rightarrow 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

\frac{sin ( x )}{cos ( x ) + sin ( x )} = 11

\frac{1 + cos ( a )}{sin ( a )} = cot (\frac{a}{s})

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

8 \cdot sin^{4} (θ) = cos (4 θ) + 4 \cdot cos (2 θ) - 3

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

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