Question

cos20°cos40°cos60°cos80°=1/16

Answer 1

The trick is to multiply by sin(20°) and repeatedly apply the double-angle identity sin(2x)=2sin(x)cos(x).

Let x = cos(20°)cos(40°)cos(80°).

x sin(20°) = sin(20°)cos(20°)cos(40°)cos(80°)
= 1/2 sin(40°)cos(40°)cos(80°)
= 1/4 sin(80°)cos(80°)
= 1/8 sin(160°)
= 1/8 sin(20°).

Therefore, x = 1/8.

then cos60x1/8=1/16

Answer 2

Answer:

Step-by-step explanation:

Bcz 4Cosa.cos(60-a).cos(60+a)=cos3a