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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

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

Use the Double Angle identity:

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

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

Use the Double Angle identity:

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

= sin (2 \cdot 2 x)

Simplify

= sin (4 x)

= sin (4 x)

We showed that the two sides could take the same form

\Rightarrow True

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

- 2 tan^{2} (0) = 2 tan (0)

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

csc^{2} (x) (sin^{2} (x) - 1) = - cot^{2} (x)

cos (3 x) = cos (x) (4 cos^{2} (x) - 3)

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