计算cos(π/5)cos(2π/5)的值

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计算cos(π/5)cos(2π/5)的值

计算cos(π/5)cos(2π/5)的值
计算cos(π/5)cos(2π/5)的值

计算cos(π/5)cos(2π/5)的值
分子乘以2sin(π/5)分母也乘以2sin(π/5)可得
sin(π/5)cos(π/5)cos(2π/5)/sin(π/5)
=1/2sin(2π/5)cos(2π/5)/sin(π/5)
=1/4sin(4π/5)/sin(π/5)
=1/4sin(π-π/5)/sin(π/5)
=1/4sin(π/5)/sin(π/5)
=1/4

sin(π/5)cos(π/5)cos(2π/5)/sin(π/5)=
1/2sin(2π/5)cos(2π/5)/sin(π/5)=
1/4sin(4π/5)/sin(π/5)=
1/4sin(π-π/5)/sin(π/5)=
-1/4sin(π/5)/sin(π/5)=
-1/4

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