Question

The value of cos 20° cos 40° cos 60° cos 80° is ______.

पर्याय

• `1/15`

• `1/16`

• `1/10`

• `1/16`

Answer 1

The value of cos 20° cos 40° cos 60° cos 80° is `underlinebb(1/16)`.

Explanation:

cos 20° cos 40° cos 60° cos 80°

= `cos 20^circ . cos 40^circ . 1/2 . cos 80^circ`

= `1/2[cos 20^circ cos 40^circ cos 80^circ]`

= `1/4[cos(20^circ + 40^circ) + cos(20^circ - 40^circ)] cos 80^circ`

= `1/4[cos(60^circ) + cos(-20^circ)] cos 80^circ`

= `1/4[1/2 cos 80^circ +  cos 20^circ cos 80^circ]`

= `1/8 cos 80^circ + 1/4 . 1/2 . 2  cos 20^circ cos 80^circ`

= `1/8 cos 80^circ + 1/8 [cos(20 + 80) + cos(20 - 80)]`

= `1/8 cos 80^circ + 1/8[cos 100^circ +  cos(-60)^circ]`

= `1/8 [cos 80^circ + [cos(180^circ - 80^circ)] + 1/8 xx 1/2`

= `1/8[cos 80^circ -  cos 80^circ] + 1/16`

= `1/16`