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Cos75Cos15sin75sin15=

cos75cos15sin75sin15分两步 cos75cos15=1/2*(cos(75+15)+cos(75-15)) sin75sin15=-1/2*(cos(75+15)-cos(75-15)) cos75cos15sin75sin15=-1/4 *( (cos90)²-(cos60)²) =-1/4*(0-0.25) =1/16

等于。

见图

(sin75+cos75)/(cos15-sin15) =√2×(cos45°sin75°+sin45°cos75°)/[√2×(cos45°cos15°-sin45°sin15°)] =sin(45°+75°)/cos(45°+15°) =sin120°/cos60° =(√3/2)/(1/2) =√3

(sin75+cos75)/(cos15-sin15) =√2×(cos45°sin75°+sin45°cos75°)/[√2×(cos45°cos15°-sin45°sin15°)] =sin(45°+75°)/cos(45°+15°) =sin120°/cos60° =(√3/2)/(1/2) =√3

有没有看到两个度数的和与差分别是90度和60度,利用这个关系,特殊角

cos75=sin15 ,sin255=sin(360-105), 由正弦函数周期性的sin(360-105)=-sin105=-sin(90+15)=-cos15 原式为sin15cos15+cos15sin15=2sin15cos15=sin30=1 /2

如图

cos15°+sin75°=cos(45°-30°)+sin(45°+30°)=cos45°cos30°+sin45°sin30°+sin45°cos30°+cos45°sin30°= 2 2 × 3 2 + 2 2 × 1 2 + 2 2 × 3 2 + 2 2 × 1 2 = 6 + 2 2 .故答案为: 6 + 2 2 .

和差化积公式: sin15°+sin75° =2sin[(15°+75°)/2]cos[(15°-75°)/2] =2sin45°cos(-30°) =2sin45°cos30° =2×(√2/2)×(√3/2) =√6/2 或者sin15°+sin75° =sin(45°-30°)+sin(45°+30°) =(sin45°cos30°-sin30°cos45°)+(sin45°cos30°+sin30°cos45°...

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