www.fltk.net > 求值:Cos105°Cos15°%sin105°sin15°=______

求值:Cos105°Cos15°%sin105°sin15°=______

cos105°cos15°-sin105°sin15°=cos(105°+15°)=cos120°=-cos60°=-12故答案为-12.

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

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

cos 105°=cos(45°+60°)=cos45°*cos60°-sin45°*sin60°=(-根号6+根号2)/4 cos15°=cos(45°-30°)=cos45°cos30°+sin45°sin30°=(根号6+根号2)/4

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

上式 = sin15°cos75°+cos15°sin75°=sin(15°+ 75°) = sin90°= 1

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·=0.2588190451

原式=cos(90+15)+sin(180+15) =-sin15-sin15 =-2sin(45-30) =-(sin45cos30-cos45sin30) =(√2-√6)/2

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