Saved Bookmarks
| 1. |
Cos20°cos40°cos80°=1/8 |
|
Answer» Given expression = cos 80° cos20° cos40° = (1/2) 2cos 80° cos20° cos40° Use 2 cosAcosB = cos(A+B) + cos(A-B) formula. = (1/2){ cos (80°+20°) + cos(80°–20°)}cos40° = (1/2)( cos 100° + cos 60°)cos40° = (1/2) cos 100° cos 40° + (1/2) cos60°cos40° = (1/2)(1/2)2cos100°cos40° +(1/2)(1/2)cos40° = (1/4){cos140° + cos60°}+ (1/4)cos40° = (1/4)(cos140° + cos40°) + (1/4)cos 60° = (1/4){cos(180°-40°) + cos 40) +(1/4) (1/2) But cos (180° -x) = -cos x. So, = (1/4)(-cos40°+cos40°) + 1/8 = 1/8 |
|