证明cos(pai/7)+cos(pai*3/7)+cos(pai*5/7)=0.5
问题描述:
证明cos(pai/7)+cos(pai*3/7)+cos(pai*5/7)=0.5
清顺便看一下cos[pai/(2n+1)]+cos[pai*3/(2n+1)]+.
+cos[pai*(2n-1)/*(2n+1)]=0.5是否成立,如果成立,清给予证明,
答
(方法一)cos(π/7)+cos(3π/7)+cos(5π/7)=2sin(π/7)(cos(π/7)+cos(3π/7)+cos(5π/7))/2sin(π/7)=(sin(2π/7)+sin(4π/7)-sin(2π/7)+sin(6π/7)-sin(4π/7))/2sin(π/7)=sin(6π/7)/2sin(π/7)=1/2类似地可以证...