The product of sin 30° and sin 60° is same as the product of cos 60 degrees tan 30 degrees and cos 30 degrees tan 60 degrees.

From the unit circle:

sin 30 = 1/2, cos 30 = √3 / 2, tan 30 = √3 / 3, tan 60 = √3;

sin 30 * sin 60 = (cos 60 * tan 30) * (cos 30 * tan 60)

Left side of an equation:

sin 30 * sin 60 = 1/2 * √3 / 2 = √3 / 4

Right side:

(cos 60 * tan 30) * (cos 30 * tan 60) =

= (1/2 * √3 / 3) * (√3 / 2 * √3) =

= √3 / 6 * 3 / 2 = √3 / 4

√3 / 4 = √3 / 4 (correct)