分类：教育/科学-理工学科-数学
问题：三角函数的求和我记得有个公式好像是sinx+sin2x+sin3 
我记得有个公式好像是sin x+sin 2x+sin 3x+……+sin nx=?c x+cos 2x+cos 3x+……+cos nx=?这是什么公式？
回答：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= [-c(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)