Cos 5分之πcos 5分之2π的值等于

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Cos 5分之πcos 5分之2π的值等于

利用二倍角公式:sin2θ=2sinθcosθ
cos(π/5)*cos(2π/5)
=2sin(π/5)*cos(π/5)*cos(2π/5)/[2sin(π/5)]
=sin(2π/5)*cos(2π/5)/[2sin(π/5]
=sin(4π/5)/[4sin(π/5)]
=sin(π/5)/[4sin(π/5)]
=1/4

sin(π—a)=sin a=4/5 ∴ sin a+cos a=1 a∈(0,π/2) 所以sina=4/5,而a∈(0,2分之π),所以 cosa=根号(1-sina的平方)=根号(