计算:cosπ/15×cos2π/15×cos4π/15×cos8π/15 要过程
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cosπ/15×cos2π/15×cos4π/15×cos8π/15
=(sinπ/15×cosπ/15×cos2π/15×cos4π/15×cos8π/15)/(sinπ/15)
=(1/2sin2π/15×cos2π/15×cos4π/15×cos8π/15)/(sinπ/15)
=(1/4sin4π/15×cos4π/15×cos8π/15)/(sinπ/15)
=(1/8sin8π/15×cos8π/15)/(sinπ/15)
=(1/16sin16π/15)/sin(16π/15-π)
=(1/16sin16π/15)/(-sin16π/15)
=-1/16
cosπ/15×cos2π/15×cos4π/15×cos8π/15
=(sinπ/15×cosπ/15×cos2π/15×cos4π/15×cos8π/15)/(sinπ/15)
=(1/2sin2π/15×cos2π/15×cos4π/15×cos8π/15)/(sinπ/15)
=(1/4sin4π/15×cos4π/15×cos8π/15)/(sinπ/15)
=(1/8sin8π/15×cos8π/15)/(sinπ/15)
=(1/16sin16π/15)/sin(16π/15-π)
=(1/16sin16π/15)/(-sin16π/15)
=-1/16
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