作业帮不用计算器,求(cos(π/8))^4+(cos(3π/8))^4+(cos(5π/8))^4+(cos(7π/8))^
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不用计算器,求(cos(π/8))^4+(cos(3π/8))^4+(cos(5π/8))^4+(cos(7π/8))^4的值
(cosa)^2=(cos2a+1)/2
(cosa)^2=(cos2a+1)^2/4
cos(π/8))^4=(cosπ/4+1)^2/4=[3+2√2]/8
cos(3π/8))^4=(cos3π/4+1)^2/4=[3-2√2]/8
cos(5π/8))^4=(cos5π/4+1)^2/4=[3-2√2]/8
cos(7π/8))^4=(cos7π/4+1)^2/4=[3+2√2]/8
(cos(π/8))^4+(cos(3π/8))^4+(cos(5π/8))^4+(cos(7π/8))^4
=3/2
(cosa)^2=(cos2a+1)^2/4
cos(π/8))^4=(cosπ/4+1)^2/4=[3+2√2]/8
cos(3π/8))^4=(cos3π/4+1)^2/4=[3-2√2]/8
cos(5π/8))^4=(cos5π/4+1)^2/4=[3-2√2]/8
cos(7π/8))^4=(cos7π/4+1)^2/4=[3+2√2]/8
(cos(π/8))^4+(cos(3π/8))^4+(cos(5π/8))^4+(cos(7π/8))^4
=3/2
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