8sinpai/32·cospai/32· cospai/16·cospai/8的值为？ 要解答过程 谢谢

-2\u30014\u3001-8\u300116\u3001-32\u300164\u3001\u2026\u2460

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\u6bcf\u4e2a\u6570\u90fd\u662f\u524d\u4e00\u4e2a\u6570\u7684-2\u500d
\u53ef\u4ee5\u5199\u516c\u5f0f\u7b2cn\u9879=(-2)\u7684n\u6b21\u65b9
\uff082\uff09\u7b2c\u2461\u2462\u884c\u6570\u4e0e\u7b2c\u2460\u884c\u6570\u5206\u522b\u6709\u4ec0\u4e48\u5173\u7cfb\uff1f
\u7b2c\u2461\u884c\u6570\u6bcf\u4e2a\u6570\u90fd\u662f\u7b2c\u4e00\u884c\u7684\u6570\u52a02
\u7b2c\u2462\u884c\u6570\u6bcf\u4e2a\u6570\u90fd\u662f\u7b2c\u2460\u884c\u7684\u6570\u9664\u4ee52(\u4e581/2)
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\u7b2c\u2460\u884c\u7b2c\u5341\u4e2a(-2)\u7684\u5341\u6b21\u65b9=1024
\u7b2c\u2461\u884c\u7b2c\u5341\u4e2a1024+2=1026
\u7b2c\u2462\u884c\u7b2c\u5341\u4e2a1024\u00f72=512
\u6240\u4ee5\u548c\u662f1024+1026+512=2562
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8sinpai/32·cospai/32· cospai/16·cospai/8
=4sinπ/16cosπ/16cosπ/8
=2sinπ/8cosπ/8
=sinπ/4
=√2/2

连续使用2sinacosa=sin2a

【中学生数理化】团队为您答题,祝你学习进步！
有不明白的可以追问！

8sin(π/32)·cos(π/32)· cos(π/16)·cos(π/8)

=4[2sin(π/32)·cos(π/32)] .cos(π/16)·cos(π/8)
=4sin(π/16).cos(π/16)·cos(π/8)
=2[2sin(π/16).cos(π/16)] cos(π/8)
=2sin(π/8)cos(π/8)
=sin(π/4)
=√2/2

由sin2x=2sinxcosx 可得
8sin(π/32)·cos(π/32)· cos(π/16)·cos(π/8)

=4[2sin(π/32)·cos(π/32)] .cos(π/16)·cos(π/8)
=4sin(π/16).cos(π/16)·cos(π/8)
=2[2sin(π/16).cos(π/16)] cos(π/8)
=2sin(π/8)cos(π/8)
=sin(π/4)
=√2/2
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