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$\sin\left( x \right) \cos\left( x \right)$
$\dfrac { 1 } { 2 } \sin\left( 2 x \right)$
Simplify the expression
$\color{#FF6800}{ \sin\left( x \right) } \color{#FF6800}{ \cos\left( x \right) }$
$ $ Use $ 2\sin(x)\cos(x) = \sin(2x) $ to arrange the expression $ $
$\color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ \sin\left( 2 x \right) }$
$\dfrac { 1 } { 2 } \sin\left( 2 x \right)$
Expand
$\color{#FF6800}{ \sin\left( x \right) } \color{#FF6800}{ \cos\left( x \right) }$
$ $ Convert the expression using $ \sin\left(x\right)\cos\left(y\right) = \dfrac{1}{2}\left(\sin\left(x+y\right)+\sin\left(x-y\right)\right)$
$\color{#FF6800}{ \dfrac { 1 } { 2 } } \left ( \color{#FF6800}{ \sin\left( x + x \right) } \color{#FF6800}{ + } \color{#FF6800}{ \sin\left( x - x \right) } \right )$
$\dfrac { 1 } { 2 } \left ( \sin\left( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ x } \right) + \sin\left( x - x \right) \right )$
$ $ Expand the expression $ $
$\dfrac { 1 } { 2 } \left ( \sin\left( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right) + \sin\left( x - x \right) \right )$
$\dfrac { 1 } { 2 } \left ( \sin\left( 2 x \right) + \sin\left( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ x } \right) \right )$
$ $ Expand the expression $ $
$\dfrac { 1 } { 2 } \left ( \sin\left( 2 x \right) + \sin\left( \color{#FF6800}{ 0 } \right) \right )$
$\dfrac { 1 } { 2 } \left ( \sin\left( 2 x \right) + \color{#FF6800}{ \sin\left( 0 \right) } \right )$
$\sin(0) $ is $ 0$
$\dfrac { 1 } { 2 } \left ( \sin\left( 2 x \right) + \color{#FF6800}{ 0 } \right )$
$\dfrac { 1 } { 2 } \left ( \sin\left( 2 x \right) \color{#FF6800}{ + } \color{#FF6800}{ 0 } \right )$
$ $ 0 does not change when you add or subtract $ $
$\dfrac { 1 } { 2 } \sin\left( 2 x \right)$
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