Is ((1-cos(4x)+sin(4x)))/((1+cos(4x)+sin(4x)))=3sin(2x) ?

The answer to whether ((1-cos(4x)+sin(4x)))/((1+cos(4x)+sin(4x)))=3sin(2x) is False

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prove ((1-cos(4x)+sin(4x)))/((1+cos(4x)+sin(4x)))=3sin(2x)

prove

\frac{( 1 - cos ( 4 x ) + sin ( 4 x ) )}{( 1 + cos ( 4 x ) + sin ( 4 x ) )} = 3 sin (2 x)

False

Solution steps

\frac{1 - cos ( 4 x ) + sin ( 4 x )}{1 + cos ( 4 x ) + sin ( 4 x )} = 3 sin (2 x)

Show that the two sides are not equal

For

\frac{1 - cos ( 4 x ) + sin ( 4 x )}{1 + cos ( 4 x ) + sin ( 4 x )} = 3 sin (2 x)

plug in

x = 1

\frac{1 - cos ( 4 \cdot 1 ) + sin ( 4 \cdot 1 )}{1 + cos ( 4 \cdot 1 ) + sin ( 4 \cdot 1 )} = - 2.18503 \dots

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

Refine to a decimal form

= - 2.18503 \dots

3 sin (2 \cdot 1) = 2.72789 \dots

3 sin (2 \cdot 1)

Refine to a decimal form

= 2.72789 \dots

The two sides are not equal

\Rightarrow False

Is ((1-cos(4x)+sin(4x)))/((1+cos(4x)+sin(4x)))=3sin(2x) ?
The answer to whether ((1-cos(4x)+sin(4x)))/((1+cos(4x)+sin(4x)))=3sin(2x) is False