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

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

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

prove

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

True

Solution steps

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

Manipulating left side

2 sin (4 x)

Rewrite using trig identities

2 sin (4 x)

= 2 sin (2 \cdot 2 x)

Use the Double Angle identity:

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

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

Simplify

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

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

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

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