作业帮函数 (4 20:28:50)
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/22 02:42:35
函数 (4 20:28:50)
cos^4 (π /8)+cos^4(3π/8)+cos^4(5π/8)+cos^4(7π/8) =
cos^4 (π /8)+cos^4(3π/8)+cos^4(5π/8)+cos^4(7π/8) =
cos^4 (π /8)+cos^4(3π/8)+cos^4(5π/8)+cos^4(7π/8) =
先用诱导公式进行转换
=cos^4 (π /8)+cos^4(3π/8)+cos^4(π-3π/8)+cos^4(π-π/8)
=cos^4 (π /8)+cos^4(3π/8)+cos^4(3π/8)+cos^4(π/8)
=2cos^4(π /8)+2cos^4(3π/8)
=2cos^4(π/8)+2cos^4(π/2-π/8)
=2cos^4(π/8)+2sin^4(π/8)
=2[sin²(π/8)+cos²(π/8)]²-4sin²(π/8)cos²(π/8)
=2-sin²π/4=3/2
其实有些步骤可以跳过不些~不过为了清楚些,我还是都写上了
先用诱导公式进行转换
=cos^4 (π /8)+cos^4(3π/8)+cos^4(π-3π/8)+cos^4(π-π/8)
=cos^4 (π /8)+cos^4(3π/8)+cos^4(3π/8)+cos^4(π/8)
=2cos^4(π /8)+2cos^4(3π/8)
=2cos^4(π/8)+2cos^4(π/2-π/8)
=2cos^4(π/8)+2sin^4(π/8)
=2[sin²(π/8)+cos²(π/8)]²-4sin²(π/8)cos²(π/8)
=2-sin²π/4=3/2
其实有些步骤可以跳过不些~不过为了清楚些,我还是都写上了