SOLUTION: Find the value of {{{sum(cos(pi(k-5)/20), k = 0, 20)/sum(sin((k*pi)/20), k = 0, 20)}}}.
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Question 457926: Find the value of .
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
We can use the sum/difference formulas for cosine to simplify the expression to
} = \sqrt{2} + \sqrt{2}\frac{ \sum_{k=0}^{20} \cos{\frac{k\pi}{20}}}{\sum_{k=0}^{20} \sin{\frac{k\pi}{20}})
Note that the expression 
is equal to zero, because if you were to draw all the angles on a unit circle, you would see that there are corresponding pairs of angles that add up to zero, since cos x = -cos (pi - x). The denominator of the fraction is some positive number because the sine of each angle is either positive or zero. Therefore the entire expression is equal to 
.
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