Ta có: ∀α thì:cotα−cot2α=cosαsin2α−cos2αsinαsinαsin2α=sinαsinαsin2α=1sin2αSuy ra:$\sum_{k=1}^n\frac{1}{\sin2^nx}=\sum_{k=1}^n(\cot2^{n-1}x-\cot2^nx)=\cot x-\cot2^nx$
Ta có: ∀α thì:cotα−cot2α=cosαsin2α−cos2αsinαsinαsin2α=sinαsinαsin2α=1sin2αSuy ra:$\sum_{k=1}^n\frac{1}{\sin2^kx}=\sum_{k=1}^n(\cot2^{k-1}x-\cot2^kx)=\cot x-\cot2^nx$