`sin 12^(@) sin 48^(@) sin 54^(@)` is equal to

Options

A. `(1)/( 16)`
B. `(1)/(32)`
C. `(1)/(8)`
D. `(1)/(4)`

Explanation

To find the value of \( \sin 12^\circ \sin 48^\circ \sin 54^\circ \), we can use trigonometric identities to simplify the expression. Here’s a step-by-step solution:

### Step 1: Use the identity for product of sines
We can express the product of two sine functions using the identity:
\[ \sin A \sin B = \frac{1}{2} [\cos(A - B) - \cos(A + B)] \]
We will first simplify \( \sin 12^\circ \sin 48^\circ \).
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