Simplify
\[4 \sin x \sin (60^\circ - x) \sin (60^\circ + x).\]The answer will be a trigonometric function of some simple function of $x,$ like "$\cos (2x)$" or "$\sin (x^3)$".
Question:
Simplify
\[4 \sin x \sin (60^\circ - x) \sin (60^\circ + x).\]The answer will be a trigonometric function of some simple function of $x,$ like "$\cos (2x)$" or "$\sin (x^3)$".
Answer:
Let's think step by step.

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\sin 3x
Simplify
\[4 \sin x \sin (60^\circ - x) \sin (60^\circ + x).\]The answer will be a trigonometric function of some simple function of $x,$ like "$\cos (2x)$" or "$\sin (x^3)$".
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