cos40°+cos60°+cos80°+cos160°怎样求值?

3个回答

  • 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