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2cos ""(pi)/(13)cos""(9pi)/(13)+cos""(3p...

`2cos ""(pi)/(13)cos""(9pi)/(13)+cos""(3pi)/(13)+cos""(5pi)/(13)=0`

A

`-1`

B

0

C

1

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`2cos.(pi)/(13).cos.(9pi)/(13)+cos.(3pi)/(13)+cos.(5pi)/(13)`
`=2cos.(pi)/(13).cos.(9pi)/(13)+2cos.(4pi)/(13)cos.(pi)/(13)`
`=2cos.(pi)/(13)[cos.(9pi)/(13)+cos.(4pi)/(13)]`
`=2cos.(pi)/(13)[2cos.(pi)/(2).cos.(5pi)/(26)]=0" "[because cos.(pi)/(2)=2]`
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