Is 2sin(z)cos(z)=sin(2z) ?

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

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prove 2sin(z)cos(z)=sin(2z)

prove

2 sin (z) cos (z) = sin (2 z)

True

Solution steps

2 sin (z) cos (z) = sin (2 z)

Manipulating right side

sin (2 z)

Rewrite using trig identities

sin (2 z)

Rewrite as

= sin (z + z)

Use the Angle Sum identity:

sin (s + s) = sin (s) cos (s) + cos (s) sin (s)

= sin (z) cos (z) + cos (z) sin (z)

= sin (z) cos (z) + cos (z) sin (z)

Simplify

sin (z) cos (z) + cos (z) sin (z) : 2 sin (z) cos (z)

sin (z) cos (z) + cos (z) sin (z)

Add similar elements:

sin (z) cos (z) + cos (z) sin (z) = 2 sin (z) cos (z)

= 2 sin (z) cos (z)

= 2 sin (z) cos (z)

We showed that the two sides could take the same form

\Rightarrow True

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9 sin (2 x) sin (x) = 9 cos (x)

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