关于三角函数的小题~

cos40°+cos60°+cos80°+cos160°可化简为A.0 B.1/2 C.1/2+2cos20° D.-1

热心网友

Bcos40°+cos60°+cos80°+cos160=cos(60°-20°)+cos60°+cos(60°+20°)+cos(180°-20°)=2cos60°*cos20°+cos60°+cos(180°-20°)=cos20°+1/2-cos20°=1/2

热心网友

cos40+cos60+cos80+cos160= cos(60-20)+cos60+cos(60+20)+cos(180-20)= cos60cos20+sin60sin20+cos60+cos60cos20-sin60sin20+cos180cos20+ sin180sin20=1/2 cos20 + 1/2 + 1/2 cos20 -cos20 +0=1/2参考公式：cos(A+B) = cosAcosB - sinAsinBcos(A-B) = cosAcosB + sinAsinB