84年學力測驗考題 相關單元：2-3-4

cos74°-cos14°等於下列那些式子?
(A)cos60° (B)2sin30°sin44° (C)2cos30°cos44° (D)sin16°-sin76°
(E)sin164°+cos166° 解答：(D)(E)

<Sol.>
(A) (╳) cos60°=cos(74°-14°)=cos74°cos14°+sin74°sin14°
(B) (╳) 2sin30°sin44°=-[cos(44°+30°)-cos(44°-30°)]=-(cos74°-cos14°)
=-cos74°+cos14°
(C) (╳) 2cos30°cos44°=cos(44°+30°)+cos(44°-30°)=cos74°+cos14°
(D) (○) sin16°-sin74°=cos(90°-16°)-cos(90°-16°)=cos74°-cos14°
(E) (○) sin164°+cos166°=sin(180°-164°)-cos(180°-166°)=sin16°-cos14°
= cos(90°-16°)-cos14°=cos74°-cos14°
[註] cos74°-cos14°=-2sinsin=-2sin44°sin30°=-sin44°