cos 40 cos 100 cos 160
Answers
Answered by
3
Answer:
= (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
Similar questions