Sin 48º + sin 12°

To find the value of \( \sin 48° + \sin 12° \), we will need to use trigonometric identities.

We know that \( \sin (A + B) = \sin A \cos B + \cos A \sin B \).

We can rewrite \( \sin 48° + \sin 12° \) as \( \sin (30° + 18°) + \sin (30° - 18°) \).

Applying the sum and difference identities:

\( \sin (30°) \cos (18°) + \cos (30°) \sin (18°) + \sin (30°) \cos (18°) - \cos (30°) \sin (18°) \)

Now, simplify:

\( 2\sin(30°) \cos (18°) \)

Knowing that \( \sin 30° = \frac{1}{2} \) and \( \cos 18° = \frac{\sqrt{5} - 1}{4} \), we have

\( 2 \cdot \frac{1}{2} \cdot \frac{\sqrt{5} - 1}{4} = \frac{\sqrt{5} - 1}{4} \)

Therefore, \( \sin 48° + \sin 12° = \frac{\sqrt{5} - 1}{4} \).