Question

高中数学题经典题型是什么?

Answer 1

1、A，B，C为三角形内角，已知1+cos2A-cos2B-cos2C=2sinBsinC，求角A？

解:1+cos2A-cos2B-cos2C=2sinBsinC

2cos²A-1-2cos²B+1+2sin²C=2sinBsinC

cos²A-cos²B+sin² (A+B)=sinBsinC

cos²A-cos²B+sin²Acos²B+2sinAcosAsinBcosB+cos²Asin²B=sinBsinC

cos²A-cos²Acos²B+2sinAcosAsinBcosB+cos²Asin²B=sinBsinC

2cos²AsinB+2sinAcosAcosB=sin(180-A-B)

2cosA(cosAsinB+sinAcosB)-sin(A+B)=0

Sin(A+B)(2cosA-1)=0

cosA=1/2

A=60。

2、计算cos20°-cos40°+cos60°+cos100°

=cos20°-cos40°-cos80°+1/2

=cos20°-cos40°-cos(20°+60°)+1/2

=cos20°-cos40°+sin20°sin60°-cos20°cos60°+1/2

=cos20°-cos40°-1/2cos20°+√3/2sin20°+1/2

=1/2cos20°+√3/2sin20°-cos40°+1/2

=cos(60°-20°)-cos40°+1/2

=cos40°-cos40°+1/2

=1/2。