cos2π/7cos4π/7cos6π/7=?

chjxjs20052022-10-04 11:39:543条回答

已提交，审核后显示！提交回复

minheyan 共回答了26个问题 | 采纳率96.2%: cos6π/7=-cosπ/7故cos2π/7cos4π/7cos6π/7=-cosπ/7cos2π/7cos4π/7然后乘上sinπ/7,有-sinπ/7*cosπ/7*cos2π/7*cos4π/7=-1/2sin2π/7*cos2π/7*cos4π/7=-1/4sin4π/7*cos4π/7=-1/8sin8π/7=1/8sinπ/7然...; 1年前

黄兔子共回答了2624个问题 | 采纳率: cos2π/7cos4π/7cos6π/7
=(8sin2π/7cos2π/7cos4π/7cos6π/7)/(8sin2π/7)
=(4sin4π/7cos4π/7cos6π/7)/(8sin2π/7)
=(2sin8π/7cos6π/7)/(8sin2π/7)
=(2sinπ/7cosπ/7)/(8sin2π/7)
=(sin2π/7)/(8sin2π/7)
=1/8; 1年前

看山水无痕共回答了57个问题 | 采纳率: cos2π/7cos4π/7cos6π/7
=cos6π/7cos2π/7cos4π/7
=-cosπ/7cos2π/7cos4π/7
=-[2sinπ/7cosπ/7cos2π/7cos4π/7]/(2sinπ/7)
=-[sin2π/7cos2π/7cos4π/7]/(2sinπ/7)
=-[2sin2π/7cos2π/7cos4π/7]/(4sinπ/...; 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

1年前查看全部

cos2π/7cos4π/7cos8π/7要过程 lyalypyongyuan1年前3: 英俊美少年共回答了13个问题 | 采纳率92.3%

8sin2π/7cos2π/7cos4π/7cos8π/7/(8sin2π/7)
=4sin4π/7cos4π/7cos8π/7/(8sin2π/7)
=2sin8π/7cos8π/7/(8sin2π/7)
=sin16π/7/(8sin2π/7)
=sin2π/7/(8sin2π/7)
=1/8

1年前查看全部