Thursday, 20 July 2017

trigonometry - General Sine and Cosine formula for sum of a finite number of angles

I was wondering is there is a general formula for sin(x1+x2+x3+...+xn) as well as for the cosine function. I know that sin(x1+x2)=sin(x1)cos(x2)+cos(x1)sin(x2) and cos(x1+x2)=cos(x1)cos(x2)sin(x1)sin(x2) But I want to find a general formula for the sum of a finite number of angles for the Sine and the cosine but I didn't noticed any pattern. I suspect that it may have a recursive pattern. Any suggestions and hints (not answers) will be appreciated.

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