Question

sin 12° sin 48° sin 54° is equal to ______.

Options

• `1/16`

• `1/32`

• `1/8`

• `1/4`

Answer 1

sin 12° sin 48° sin 54° is equal to `underlinebb(1/8)`.

Explanation:

sin 12° sin 48° sin 54° 

= `1/2[cos 36^circ -  cos 60^circ]cos 36^circ`

= `1/2[(sqrt(5) + 1)/4 - 1/2][(sqrt(5) + 1)/4]`

= `1/2[(sqrt(5) - 1)/4][(sqrt(5) + 1)/4]`

= `(5 - 1)/32`

= `4/32`

= `1/8`