cos五分之派乘以cos五分之二派等于多少

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cos五分之派乘以cos五分之二派等于多少

cos五分之派乘以cos五分之二派等于多少
cos五分之派乘以cos五分之二派等于多少

cos五分之派乘以cos五分之二派等于多少
解法一:
直接查函数表或用计算器:
cosπ/5*cos2π/5=cos36°*cos72°.
=0.8090*0.3090
=0.2499.
∴原式=0.25.
解法二:应用积化和差公式:
(1/2)*2cosπ/5*cos2π/5=(1/2)[cos(π/5+2π/5)+cos(π/5-2π/5)].
=(1/2)[cos3π/5+cos(-π/5] .
=(1/2)(cos108+cos36).
=(1/2)(-cos72+cos36)
=(1/2)(-0.3090+0.8090)
=(1/2)*0.5
∴原式=0.25.