Prove that `sin 12^(@) sin18^(@)sin42^(@) sin48^(@) sin 72^(@) sin78^(@)=(cos18^(@))/(32)`.

Explanation

To prove that

\[ \sin 12^\circ \sin 18^\circ \sin 42^\circ \sin 48^\circ \sin 72^\circ \sin 78^\circ = \frac{\cos 18^\circ}{32}, \]

we will start with the left-hand side and manipulate it step by step.

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