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sin15°+sin75°=?

1、本题可以利用诱导公式、辅助角公式或二倍角公式与两角和与差公式求解。 2、解法1:sin15°+sin75°=sin15°+cos15°=√2sin(45°+15°)=√2sin60°=√6/2. 解法2:原式=sin15°+cos15°=√(sin15°+cos15°)²=√(1+sin30°)=√(3/2)=√6/2. 解法3:原式=sin...

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°...

解:sin75°+sin15° =2sin((75°+15°)/2)cos((75°-15°)/2) (应用和差化积公式) =2sin45°cos30° =2(√2/2)(√3/2) =√6/2。

sin15sin30sin75 =(1/2)sin15sin(90-15) =(1/2)sin15cos15 =(1/2)*[(1/2)*2sin15cos15] =(1/4)sin30 =1/8

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

sin105° = sin(45°+60°) = sin45°cos60°+cos45°sin60° = √2/2*½+√2/2*√3/2 = √2/4+√6/4 = (√2+√6)/4 sin75° = sin(45°+30°) = sin45°cos30°+cos45°sin30° = √2/2*√3/2+√2/2*½ = (√2+√6)/4 sin15° = sin(45°-30°) = sin45°co...

sin15度*sin30度*sin75度 =sin(45-30)sin30sin(45+30) =sin30(sin45cos45-sin30cos45)(sin45cos30+sin30cos45) =1/2(根号6-根号2)/4*(根号6+根号2)/4 =4/32 =1/8

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

sinA=cos (90-A) sin75=cos (90-75)=cos15

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