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

求值:Cos105°Cos15°%sin105°sin15°=______

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

=-根3/2

cos105°=cos(60°+45°)=cos60°cos45°-sin60°sin45°= 1 2 × 2 2 - 3 2 × 2 2 = 2 - 6 4 .故答案为: 2 - 6 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

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°,

sin15度cos75度+cos15度sin105度 =sin15度cos75度+cos15度sin(180-105)度 =sin15度cos75度+cos15度sin75度 =sin(15+75)度 =sin90度 =1

sin15°cos75°+cos15°sin105°=sin15°*sin15°+cos15°*cos15°=1 注意周期性即可

sin105+sin15=sin(90+15)+sin15=sin90*cos15+cos90*sin15+sin15 =cos15+sin15=√2(√2/2*cos15+√2/2*sin15)=√2(sin45*cos15+cos45*sin15) =√2sin60=√2*√3/2=√6/2 希望帮助到你,望采纳,谢谢!

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...

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

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