计算cosπ/8的四次方+cos3π/8的四次方+5π/8的四次方+cos7π/8的四次方之和
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![计算cosπ/8的四次方+cos3π/8的四次方+5π/8的四次方+cos7π/8的四次方之和](/uploads/image/z/3014538-42-8.jpg?t=%E8%AE%A1%E7%AE%97cos%CF%80%2F8%E7%9A%84%E5%9B%9B%E6%AC%A1%E6%96%B9%2Bcos3%CF%80%2F8%E7%9A%84%E5%9B%9B%E6%AC%A1%E6%96%B9%2B5%CF%80%2F8%E7%9A%84%E5%9B%9B%E6%AC%A1%E6%96%B9%2Bcos7%CF%80%2F8%E7%9A%84%E5%9B%9B%E6%AC%A1%E6%96%B9%E4%B9%8B%E5%92%8C)
计算cosπ/8的四次方+cos3π/8的四次方+5π/8的四次方+cos7π/8的四次方之和
计算cosπ/8的四次方+cos3π/8的四次方+5π/8的四次方+cos7π/8的四次方之和
计算cosπ/8的四次方+cos3π/8的四次方+5π/8的四次方+cos7π/8的四次方之和
cos7π/8
=-cos(π-7π/8)
=-cosπ/8
同理cos5π/8=-cos3π/8
又cos3π/8=sin(π/2-3π/8)=sinπ/8
所以cosπ/8的四次方+cos3π/8的四次方+5π/8的四次方+cos7π/8的四次方
=2(cosπ/8的四次方+cos3π/8的四次方)
=2(cosπ/8的四次方+sinπ/8的四次方)
=2[(cosπ/8的二次方+sinπ/8的二次方)^2-2cosπ/8的二次方*sinπ/8的二次方]
=2[1-(sinπ/4)^2/2]
=2*(1-1/4)
=3/2
3/2