Question

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 .

Answer 1

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 )