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sin105°Cos105°+Cos75°sin75°=

显然sin105°=sin(180°-105°)=sin75° 而cos105°= -cos(180°-105°)= -cos75° 所以 sin105°cos105°+cos75°sin75° = -sin75°cos75°+cos75°sin75° =0

如图

sin15°=sin(45°-30°)=sin45cos30-cos45sin30=√2/2*√3/2-√2/2*1/2=(√6-√2)/4 sin75°=sin(45°+30°)=sin45cos30+cos45sin30=√2/2*√3/2+√2/2*1/2=(√6+√2)/4 sin105°=sin(180°-75°)=sin75°=(√6+√2)/4 cos15°=sin(90°-15°)=sin75°=(√6+√2)/4 cos75°=si...

sin105°cos105°=sin(60°+45°)cos(60°+45°)=(sin60°cos45°+cos60°sin45°)(cos60°cos45°-sin60°sin45°)=( 3 2 × 2 2 + 1 2 × 2 2 )( 1 2 × 2 2 - 3 2 × 2 2 )=- 1 4 故答案为- 1 4 .

sin105=cos15 而 cos30=2*(cos15)^2-1=(根号3)/2 把那个cos15 解出来 取正值 (根6+根2)/4 拓展资料: sin75°cos105°-sin105°sin15°的值等于 原式=sin75cos(180-75)-sin(180-75)sin(90-75) =sin75(-cos75)-sin75cos75 =-sin75cos75-sin75cos75 ...

sin15°=(√6-√2)/4,cos15°=(√6+√2)/4,tan15°=2-√3, sin75°=(√6+√2)/4,cos75°=(√6-√2)/4,tan75°=2+√3, sin105°=sin75°, cos105°=-cos75°, tan105°=-tan75°,

解:sin105°=sin(180°-105°)=sin75°

B:-1/2把cos15°换成sin75° 再利用 sin(a+b)来做就行了

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°cos75°+cos15°sin105°=sin15°cos75°+cos15°sin75°=sin(15°+75°)=sin90°=1故答案为:1

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