Is 2sin(θ)cos(θ)=sin(2θ) ?

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

prove 2sin(θ)cos(θ)=sin(2θ)

prove

2 sin (θ) cos (θ) = sin (2 θ)

True

Solution steps

2 sin (θ) cos (θ) = sin (2 θ)

Manipulating right side

sin (2 θ)

Rewrite using trig identities

sin (2 θ)

Rewrite as

= sin (θ + θ)

Use the Angle Sum identity:

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

= sin (θ) cos (θ) + cos (θ) sin (θ)

= sin (θ) cos (θ) + cos (θ) sin (θ)

Simplify

sin (θ) cos (θ) + cos (θ) sin (θ) : 2 sin (θ) cos (θ)

sin (θ) cos (θ) + cos (θ) sin (θ)

Add similar elements:

sin (θ) cos (θ) + cos (θ) sin (θ) = 2 sin (θ) cos (θ)

= 2 sin (θ) cos (θ)

= 2 sin (θ) cos (θ)

We showed that the two sides could take the same form

\Rightarrow True

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