证1/2+求和cosk(x-x0)=(sin(n)+1/2)(x-x0)/2*sin((x-x0)/2)_其他解答

证1/2+求和cosk(x-x0)=(sin(n)+1/2)(x-x0)/2*sin((x-x0)/2)

人气：482 ℃　时间：2022-01-12 22:32:17

解答

左边只需要乘以2*sin((x-x0)/2),利用积化和差公式,
左边*2 sin((x-x0)/2)
=sin ((x-x0)/2)-sin((x-x0)/2)+sin(3(x-x0)/2)-sin(3(x-x0)/2)+sin(3(x-x0)/2)
+...-sin((2n-1)*(x-x0)/2)+sin((2n+1)*(x-x0)/2)
=sin[(n+1/2)*(x-x0)]
证得结果