Prove that sin 20 × sin40 × sin60 × sin80 = 3/16

Answer: The sine function in trigonometry is defined as the ratio of the opposite side’s length to the hypotenuse’s length in a right-angled triangle. The sine function finds the unknown angle or sides of a right triangle.

Let us assume, that LHS

= sin 20 × sin 40 × sin60 × sin80

= sin60 [sin20 × sin40 × sin80]

= √3/2[sin20 × sin(60 – 20) × sin(60 + 20)]

= √3/2[sin 3(20)/4]

= √3/2[sin 60/4]

= √3/2[√3/2 × 4]

= √3/2 × √3/8

= 3/16

= RHS

Therefore,  LHS = RHS

Hence proved.