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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

= sin^{3} (2 x)

We showed that the two sides could take the same form

\Rightarrow True

81 - 9 (3 sin (x))^{2} = 11

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

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

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

3 tan (A) = \frac{1}{tan ( B )}

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