sin5°sin25°-sin95°sin65°的值是A,1/2 B,-1/2 C,根号3/2 D,-根号3/2

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sin5°sin25°-sin95°sin65°的值是A,1/2 B,-1/2 C,根号3/2 D,-根号3/2
sin5°sin25°-sin95°sin65°的值是
A,1/2 B,-1/2 C,根号3/2 D,-根号3/2

sin5°sin25°-sin95°sin65°的值是A,1/2 B,-1/2 C,根号3/2 D,-根号3/2
sin5·×sin25·-sin95·×sin65· =sin5·×cos65·-sin85·×sin65· =sin5·×cos65·-cos5·×sin65· =sin(5·-65·) =sin(-60·) =-sin60· =-√3/2

D
sin5°sin25°-sin95°sin65°=sin5°sin25°-cos5°cos25°=-cos(5°+25°)=-cos30°=-根号3/2

原式=sin5°sin25°-cos5°cos25°=-(cos5°cos25°-sin5°sin25°)
=-cos(5°+25°)=-cos30° 故答案为D