Find the value of cos-5-cos2-5-cos6-5-cos7-5

#160;cosπ #160;/ 5 #160; +cos 2π #160;/ 5 #160; +cos 6π #160;/ 5 #160; +cos 7π #160;/ 5 #160; rearranging #160;=cosπ #160;/ 5 ...

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Multiplication with Vectors

Find the valu...

Question

Find the value of $cos \frac{π}{5} + cos \frac{2 π}{5} + cos \frac{6 π}{5} + cos \frac{7 π}{5}$

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Solution

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cos \frac{π}{15} . cos \frac{2 π}{15} . cos \frac{3 π}{15} . cos \frac{4 π}{15} . cos \frac{5 π}{15} . cos \frac{6 π}{15} . cos \frac{7 π}{15}

cos \frac{π}{7} + cos \frac{2 π}{7} + cos \frac{3 π}{7} + cos \frac{4 π}{7} + cos \frac{5 π}{7} + cos \frac{6 π}{7} + cos \frac{7 π}{7}

cos \frac{π}{7} + cos \frac{2 π}{7} + cos \frac{3 π}{7} + cos \frac{4 π}{7} + cos \frac{5 π}{7} + cos \frac{6 π}{7} + cos \frac{7 π}{7} =

c o s \frac{2 π}{3} - c o s π + c o s \frac{4 π}{3} - c o s \frac{5 π}{3} + c o s 2 π - c o s \frac{7 π}{3} + . . . . + c o s \frac{40 π}{3} - c o s \frac{41 π}{3} = k

sin \frac{6 π}{5} + i (1 + cos \frac{6 π}{5})

\frac{i - 1}{i (1 - cos \frac{2 π}{5}) + sin \frac{2 π}{5}}

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