Saturday, September 8, 2018

trigonometry - How to evaluate sumn1k=1fracsin(ktheta)sintheta



How to evaluate n1k=1sin(kθ)sinθ



Any help ? I tried to use difference method. But I'm not getting there.


Answer



HINT:




Use the Prosthaphaeresis Formula,



cos((k1)θ)cos((k+1)θ)=2sin(kθ)sin(θ)



and then sum the resulting telescoping series.


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