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

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

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

prove

2 (sin (2 y) cos (2 y)) = sin (4 y)

True

Solution steps

2 sin (2 y) cos (2 y) = sin (4 y)

Manipulating left side

2 sin (2 y) cos (2 y)

Rewrite using trig identities

2 sin (2 y) cos (2 y)

Use the Double Angle identity:

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

= sin (2 \cdot 2 y)

Simplify

= sin (4 y)

= sin (4 y)

We showed that the two sides could take the same form

\Rightarrow True

csc^{2} (θ) \cdot (sin^{2} (θ)) = 1

tan (b) cos (b) + cot (b) cos (b) = csc (b)

1 + cot^{2} (z) = csc^{2} (z)

csc (x) - 1 = \frac{2 sin ( x )}{sin ( x )}

2 sin^{2} (θ) - cos (2 θ) = 1

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