The value of sin 12°. sin48°.sin54

To find the value of sin 12°. sin 48°. sin 54°, we can use the trigonometric identity:

sin A . sin B = 1/2 [cos(A - B) - cos(A + B)]

Let's substitute the given values into the formula:

sin 12° . sin 48° . sin 54° = 1/2 [cos(48° - 12°) - cos(48° + 12°)] . sin 54°

Simplifying further:

sin 12° . sin 48° . sin 54° = 1/2 [cos 36° - cos 60°] . sin 54°

Now, we need to find the values of cos 36°, cos 60°, and sin 54°. We can use a calculator or trigonometric tables to determine these values.

cos 36° ≈ 0.809 cos 60° = 1/2 sin 54° ≈ 0.809

Substituting these values back into the equation:

sin