三角函数的求和我记得有个公式好像
A =sin x+sin 2x+sin 3x+……+sin nx
A*2*sin(x/2)
= [2*sin(x/2)]*sin x +[2*sin(x/2)]*sin 2x +。。。。+[2*sin(x/2)]*sin nx
= [-cos(3x/2)+cos(x/2)] +[-cos(5x/2)+cos(3x/2)] +。 。。+
+[-cos(n+1/2)x +cos(n-1/2)x]
===> sin x+sin 2x+sin 3x+……+sin nx
= [-cos(n+1/2)x +cos(x/2)]/2sin(x/2)
B =cos x+cos 2x+cos 3x+……+c...全部
A =sin x+sin 2x+sin 3x+……+sin nx
A*2*sin(x/2)
= [2*sin(x/2)]*sin x +[2*sin(x/2)]*sin 2x +。。。。+[2*sin(x/2)]*sin nx
= [-cos(3x/2)+cos(x/2)] +[-cos(5x/2)+cos(3x/2)] +。
。。+
+[-cos(n+1/2)x +cos(n-1/2)x]
===> sin x+sin 2x+sin 3x+……+sin nx
= [-cos(n+1/2)x +cos(x/2)]/2sin(x/2)
B =cos x+cos 2x+cos 3x+……+cos nx
B*2*sin(x/2) =
= [2*sin(x/2)]*cos x +[2*sin(x/2)]*cos 2x +。
。。。+[2*sin(x/2)]*cos nx
= [sin(3x/2)-sin(x/2)] +[sin(5x/2)-sin(3x/2)] +。。。
+
+[sin(n+1/2)x -sin(n-1/2)x]
===> cos x+cos 2x+cos 3x+……+cos nx
= [sin(n+1/2)x -sin(x/2)]/2sin(x/2)。收起
