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

The answer to whether sin(4x)=2sin(2x) is False

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

prove

sin (4 x) = 2 sin (2 x)

False

Solution steps

sin (4 x) = 2 sin (2 x)

Show that the two sides are not equal

For

sin (4 x) = 2 sin (2 x)

plug in

x = 1

sin (4 \cdot 1) = - 0.75680 \dots

sin (4 \cdot 1)

Refine to a decimal form

= - 0.75680 \dots

2 sin (2 \cdot 1) = 1.81859 \dots

2 sin (2 \cdot 1)

Refine to a decimal form

= 1.81859 \dots

The two sides are not equal

\Rightarrow False

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