cos π/15 * cos 2π/15 * cos4π/15 * cos8π/15

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cos π/15 * cos 2π/15 * cos4π/15 * cos8π/15
cos π/15 * cos 2π/15 * cos4π/15 * cos8π/15

cos π/15 * cos 2π/15 * cos4π/15 * cos8π/15
=[1/(sin π/15)]*sinπ/15 *cos π/15 * cos 2π/15 * cos4π/15 * cos8π/15
=[1/(sin π/15)]*(1/2)*sin2π/15 * cos 2π/15 * cos4π/15 * cos8π/15
=[1/(sin π/15)]*(1/4)*sin4π/15 * cos4π/15 * cos8π/15
=[1/(sin π/15)]*(1/8)*sin8π/15 * cos8π/15
=[1/(sin π/15)]*(1/16)*sin16π/15
=[1/(sin π/15)]*(1/16)*sin(π+π/15 )
=[1/(sin π/15)]*(1/16)*sinπ/15
=1/16

将分母看做1得到(cos π/15 * cos 2π/15 * cos4π/15 * cos8π/15 )/1
=(16sinπ/15 *cos 2π/15 * cos4π/15 * cos8π/15 )/16sinπ/15
=(8sin2π/15*cos 2π/15 * cos4π/1...

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将分母看做1得到(cos π/15 * cos 2π/15 * cos4π/15 * cos8π/15 )/1
=(16sinπ/15 *cos 2π/15 * cos4π/15 * cos8π/15 )/16sinπ/15
=(8sin2π/15*cos 2π/15 * cos4π/15 * cos8π/15) /16sinπ/15
=(4sin4π/15 * cos4π/15 * cos8π/15) /16sinπ/15
=(2sin8π/15 * cos8π/15) /16sinπ/15
=(sin16π/15 )/16sinπ/15
=(-sinπ/15 )/16sinπ/15 =-1/16

收起

求问一道高一数学计算题.cos(π/15)cos(2π/15)cos(4π/15)cos(8π/15) cos π/15 * cos 2π/15 * cos4π/15 * cos8π/15 计算：cos（π/5)+cos（2π/5)+cos(3π/5)+cos(4π/5) cos(π/17)*cos(2π/17)*cos(4π/17)*cos(8π/17) cos^2α+cos^2(α+π/3)-cosαcos(α+π/3)化简 cos(pai/15)×cos(2pai/15)×cos(3pai/15)×cos(4pai/15)×cos(5pai/15)×cos(6pai/15)×cos(7pai/15)求值 cos(pai/15)×cos(2pai/15)×cos(3pai/15)×cos(4pai/15)×cos(5pai/15)×cos(6pai/15)×cos(7pai/15)求值 求值:cos(π/11)cos(2π/11)cos(3π/11)cos(4π/11)cos(5π/11) 求值：cos(π/11)-cos(2π/11)+cos(3π/11)-cos(4π/11)+cos(5π/11) cos(π/11)cos(2π/11)cos(3π/11)cos(4π/11)cos(5π/11) 已知sina=15/17,cosβ= - 5/13,a∈（π/2,π）,求cos（a+β）,cos（a-β）的值.急用 cos(θ-π/2)等于cos(π/2-θ) 2cos(π/2+a)cos(π-a)化简 计算cos(π/5)cos(2π/5)的值 cos(-x-2π) 和cos(π-x) 化简 Cos(α-π) Cos(α- π/2 )如何化简 化简cos^2(A+15)+cos^2(A-15)-cos30cos2A 为什么cos(θ-2π)=cosθ,