cosπ/7cos2π/7cos3π/7=?

chengyangling2022-10-04 11:39:542条回答

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WUHAIYONG 共回答了21个问题 | 采纳率76.2%: 原式=sinπ/7*cosπ/7*cos2π/7*cos3π/7/sinπ/7
=2sinπ/7*cosπ/7*cos2π/7*cos(π-4π/7)/2sinπ/7
=sin2π/7*cos2π/7*(-cos4π/7)/2sinπ/7
=-2sin2π/7*cos2π/7*cos4π/7/4sinπ/7
=-sin4π/7*cos4π/7/4sinπ/7
=-2sin4π/7*cos4π/7/8sinπ/7
=-sin8π/7/8sinπ/7
=sinπ/7/8sinπ/7
=1/8; 1年前

sinleen 共回答了15个问题 | 采纳率: cosπ/7cos2π/7cos3π/7
=cos(π/7)cos(2π/7)cos(π/2-π/7)
=cos(π/7)cos(2π/7)sin(π/7)
=sin(2π/7)cos(2π/7)/2
=sin(4π/7)/4
运用sin2a=2sinacosa; 1年前

求值:cosπ/7cos2π/7cos3π/7cos4π/7cos5π/7cos6π/7 smooochsun1年前1: slw533 共回答了20个问题 | 采纳率90%

由诱导公式可得：cos6π/7=-cosπ/7；
cosπ/7=-cos6π/7,cos3π/7=-cos4π/7,cos5π/7=-cos2π/7
∴ cos2π/7cos4π/7cos6π/7
=-cosπ/7cos2π/7cos4π/7
=-sinπ/7cosπ/7cos2π/7cos4π/7/sinπ/7
=-1/2·sin2π/7cos2π/7cos4π/7/sinπ/7
=-1/4·sin4π/7cos4π/7/sinπ/7
=-1/8·sin8π/7/sinπ/7
=-1/8·(-sinπ/7)/sinπ/7
=1/8
而cosπ/7cos3π/7cos5π/7=(-cos6π/7)(-cos4π/7)(-cos2π/7)
=-cos2π/7cos4π/7cos6π/7=-1/8
∴原式=-1/64

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cosπ/7cos2π/7cos3π/7＝1/8是怎么推出来的?求仔细讲解 飞叶1年前2: 云端莹影共回答了11个问题 | 采纳率100%

cosπ/7cos2π/7cos3π/7
=2sinπ/7cosπ/7cos2π/7cos3π/7/2sinπ/7
=sin2π/7cos2π/7[-cos(π-3π/7)]/2sinπ/7
=-sin4π/7cos4π/7/4sinπ/7
=-sin8π/7/8sinπ/7
=sinπ/7/8sinπ/7
=1/8

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