Is 1/2 sin(2x)=sin(x)cos(x) ?

The answer to whether 1/2 sin(2x)=sin(x)cos(x) is True

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prove 1/2 sin(2x)=sin(x)cos(x)

prove

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

True

Solution steps

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

Manipulating left side

\frac{1}{2} sin (2 x)

Rewrite using trig identities

\frac{1}{2} sin (2 x)

Use the Double Angle identity:

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

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

Simplify

\frac{1}{2} \cdot 2 sin (x) cos (x) : sin (x) cos (x)

\frac{1}{2} \cdot 2 sin (x) cos (x)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Cancel the common factor:

2

= sin (x) cos (x) \cdot 1

Multiply:

cos (x) \cdot 1 = cos (x)

= sin (x) cos (x)

= sin (x) cos (x)

= sin (x) cos (x)

We showed that the two sides could take the same form

\Rightarrow True

Is 1/2 sin(2x)=sin(x)cos(x) ?
The answer to whether 1/2 sin(2x)=sin(x)cos(x) is True