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

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

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

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

\frac{sin ( 4 \cdot 1 )}{4} = - 0.18920 \dots

\frac{sin ( 4 \cdot 1 )}{4}

Refine to a decimal form

= - 0.18920 \dots

4 \cdot \frac{sin ( 1 ) cos ( 1 )}{4} = 0.45464 \dots

4 \cdot \frac{sin ( 1 ) cos ( 1 )}{4}

Refine to a decimal form

= 0.45464 \dots

The two sides are not equal

\Rightarrow False

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