Is prove-2cos(2x)*sin(2x)=sin(-4x) ?

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

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

prove

- 2 cos (2 x) \cdot sin (2 x) = sin (- 4 x)

True

Solution steps

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

Manipulating left side

- 2 cos (2 x) sin (2 x)

Rewrite using trig identities

- 2 cos (2 x) sin (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)

Manipulating right side

sin (- 4 x)

Use the negative angle identity:

sin (- x) = - sin (x)

= - sin (4 x)

We showed that the two sides could take the same form

\Rightarrow True

sec^{2} (x) + tan (x) - 1 = 0

tan (a) cot (a) = 1

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

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

tan (x) + 1 = 1

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