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find the value cos(2pi/7)+cos(4pi/7)+cos(6pi/7)

find the value cos(2pi/7)+cos(4pi/7)+cos(6pi/7)

Grade:11

1 Answers

Rinkoo Gupta
askIITians Faculty 81 Points
9 years ago
cos(2pi/7)+cos(4pi/7)+cos(6pi/7)
=1/2sin(pi/7)[2sinpi/7cos2pi/7+2sinpi/7cos4pi/7+2sinpi/7cos6pi/7]
=1/2sinpi/7[sin3pi/7+sin(-pi/7) +sin5pi/7+sin(-3pi/7) +sinpi +sin(-5pi/7)]
=1/2sinpi/7[sin3pi/7-sinpi/7+sin5pi/7-sin3pi/7+0-sin5pi/7]
=1/2sinpi/7[-sinpi/7]
=-1/2
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

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