Question

The value of sin 36° sin 72° sin 108° sin 144° is ______.

Options

• `1/4`

• `1/16`

• `3/4`

• `5/16`

Answer 1

The value of sin 36° sin 72° sin 108° sin 144° is `underlinebb(5/16)`.

Explanation:

sin 36° sin 72° sin 108° sin 144° 

= sin² 36° sin² 72°

= `1/4[(2 sin^2 36^circ)(2 sin^2 72^circ)]`

= `1/4[(1 - cos 72^circ)(1 - cos 144^circ)]`

= `1/4[(1 - sin 18^circ)(1 + cos 36^circ)]`

= `1/4[(1 - (sqrt(5) - 1)/4)(1 + (sqrt(5) + 1)/4)]`

= `5/16`