0.5
cosπ/9·cos2π/9·cos3π/9·cos4π/9 =(2sinπ/9cosπ/9·cos2π/9·cosπ/3·cos4π/9)/(2sinπ/9) =(2sin2π/9·cos2π/9·(1/2)·cos4π/9)/(4sinπ/9) =((1/2)2sin4π/9·cos4π/9)...
cos2π/9*cos4π/9*cos8π/9 =(8sin2π/9*cos2π/9*cos4π/9*cos8π/9)/(8sin2π/9) 同时乘除一个8sin2π/9原式值不变 =(4sin4π/9*cos4π/9*cos8π/9)/(8sin2π/9) 因为2sinacosa=sin2a =(...
解:16sin(π/17)cos(π/17)cos(2π/17)cos(4π/17)cos(8π/17) =8sin(2π/17)cos(2π/17)cos(4π/17)cos(8π/17) =4sin(4π/17)cos(4π/17)cos(8π/17) =2sin(8π/17)cos(8π/17...
cos2π/18+cos4π/18+cos8π/18+cos16π/18= =cos2π/18+cos4π/18+cos8π/18-cos2π/18 =cos4π/18+cos8π/18(化积) =2cos6π/18cos2π/18 =2*(1/2)*cosπ/9 =cosπ/9
原式=[(2sin7兀/2)/(2sin2兀/7)]*(cos2兀/7+cos4兀/7+cos6兀/7)=[1/(2sin2兀/7)]*(sin4兀/7+sin6兀/7-sin2兀/7+sin8兀/7-sin4兀/7)=-1/2。
原式=[sin(2π/7)*cos(2π/7)*cos(4π/7)*cos(6π/7)]/[sin(2π/7)] =[sin(4π/7)*cos(4π/7)*cos96π/7)]/[2sin(2π/7)] =[sin(8π/7)*cos(6π/7)]/[4sin(2π/7)] =[sin(π+π/7...
cos(2π/7)+cos(4π/7)+cos(6π/7) =2cos(3π/7)cos(π/7) + 2cos^(3π/7)-1 =2cos(3π/7)[cos(π/7)+cos(3π/7)]-1 =4cos(3π/7)cos(2π/7)cos(π/7)-1 =4cos(3π/7)cos(2π/7...
用积化和差公式轻松解决(pi表示 派）： 原式=1/2(cos(-2pi/5)+cos(pi))+1/2(cos(-3pi/5)+cos(pi)) =-1+1/2(cos(2pi/5)-cos(2pi/5)) =-1
