试证：cos（π/7）+cos（3π/7）+cos（5π/7）=0.5
热心网友
设 cos(π/7）+cos(3π/7）+cos(5π/7）= M两边同乘以2sin(π/7)2sin(π/7)cos(π/7) + 2sin(π/7)cos(3π/7) + 2sin(π/7)cos(5π/7) = 2Msin(π/7)利用积化和差公式：sinαcosβ=1/2*[sin(α+β)+sin(α-β)]上式化为：sin(2π/7) + sin(4π/7) - sin(2π/7) + sin(6π/7) - sin(4π/7) = 2Msin(π/7)sin(6π/7)=2Msin(π/7) sin(6π/7)=sin(π/7)所以2M=1 == M=1/2=0.5
热心网友
左边=2sin(2π/7) /2sin(2π/7) *（cos(π/7）+cos(3π/7）+cos(5π/7）) =1/2sin(2π/7) *(sin(2π/7)+ sin(4π/7)- sin(2π/7)+ sin(6π/7)- sin(4π/7)) =sin(6π/7)/ 2sin(π/7) =sin(π/7）/2sin(π/7) =1/2 ∵左边=右边∴右边=1/2