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Questions  

The value of cos2π7+cos4π7+cos6π7+cos7π7 is

a
1
b
-1
c
1/2
d
-3/2

detailed solution

Correct option is D

cos⁡2π7+cos⁡4π7+cos⁡6π7+cos⁡7π7=12sin⁡π72sin⁡π7cos⁡2π7+2sin⁡π7cos⁡4π7+2sinπ7cos6π7-1=12sin⁡π7sin⁡π73π7−sin⁡π7+sin⁡5π7−sin⁡3π7+sin7π7-sin5π7-1=12sinπ7-sinπ7-1=-12-1=-32.

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