解三角方程,cosβcos3β = cos5βcos7β积化和差之后是 1/2(cos4β + cos2β)= 1/2(cos12β + cos2β)

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解三角方程,cosβcos3β = cos5βcos7β积化和差之后是 1/2(cos4β + cos2β)= 1/2(cos12β + cos2β)

解三角方程,cosβcos3β = cos5βcos7β积化和差之后是 1/2(cos4β + cos2β)= 1/2(cos12β + cos2β)
解三角方程,cosβcos3β = cos5βcos7β
积化和差之后是 1/2(cos4β + cos2β)= 1/2(cos12β + cos2β)

解三角方程,cosβcos3β = cos5βcos7β积化和差之后是 1/2(cos4β + cos2β)= 1/2(cos12β + cos2β)
1/2(cos4β + cos2β)= 1/2(cos12β + cos2β)
即 cos12β=cos4β
12β = 2kπ ± 4β
解之得:β = kπ/4 或 β = kπ/8

积化和差,得cos2β=cos6β,再用余弦三倍角公式化为关于cos2β的方程,可求得cosβ