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.

0 解析: cos15°cos105°+sin15°sin105° =cos(15°-105°) =cos(-90°) =cos90° =0

cos15°cos105°-sin105°sin15° =cos(105°-15°) =cos(90°) =0 sin20°sin10°-cos10°sin70° =cos70°sin10°-cos10°sin70° =sin(10°-70°) =sin(-60°) =-cos(30°) =-√3/2

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

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

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

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 ...

(sin105°-√3cos105°)(√3cos15°-sin15°) =2(1/2sin105º-√3/2cos105º)*2(√3/2*cos15º-1/2sin15º) =4(sin105ºcos60º-cos105ºsin60º)(sin60ºcos15º-cos60ºsin15º) =4sin(105º-45&...

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...

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