cos40°+cos60°+cos80°+cos160°

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cos40°+cos60°+cos80°+cos160°

cos40°+cos60°+cos80°+cos160°
cos40°+cos60°+cos80°+cos160°

cos40°+cos60°+cos80°+cos160°
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 - sinAsinB
cos(A-B) = cosAcosB + sinAsinB
技巧,将非特殊角转化成特殊角与另一个角相加,然后设法消掉那个角

题呢?