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(sin75+Cos75)/(Cos15%sin15)=?

(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

sin75°=sin(45°+30°)=sin45°cos30°+cos45°sin30°=(√6+√2)/4 cos75=cos(30+45)=cos30cos45-sin30sin45=√6/4-√2/4=(√6-√2)/4 sin75+cos75=sin75+sin15=2sin(75+15)/2cos(75-15)/2=2sin45cos30=√6/2 sin75-cos75=sin75-sin15=2cos(75+15)/2sin(75-1...

等于。

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

套公式cos(A-B)=cosA*cosB+sinA*sinB 上题等于cos60=0.5

方法一:cos75°cos15°+sin75°sin15°=cos(75°-15°)=cos60°=0.5 方法二:cos75°cos15°+sin75°sin15°=sin15°cos15°+cos15°sin15°=sin15°cos15°=sin30°=0.5

sin15°cos75° =(根号6-根号2)/4X(根号6+根号2)/4 =[(根号6-根号2)X(根号6+根号2)]/16 =(6-2)/16 =1/4

cos75-cos15 =cos(45+30)-cos(45-30) =cos45cos30-sin45sin30-(cos45cos30+sin45sin30) =cos45cos30-sin45sin30-cos45cos30-sin45sin30 =-2sin45sin30 =-2*(√2)/2*1/2 =-(√2)/2

(sin75°-sin15°)(cos15°+cos75°)=[sin(90°-15°)-sin15°][cos15°+cos(90°-15°)]=(cos15°-sin15°)(cos15°+sin15°)=cos215°-sin215°=cos30°=32.故选B.

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