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The value of cos""(pi)/(11)+cos""(3pi)/(...

The value of `cos""(pi)/(11)+cos""(3pi)/(11)+cos""(5pi)/(11)+cos""(7pi)/(11)+cos""(9pi)/(11),` is

Text Solution

Verified by Experts

The correct Answer is:
`1//2`
We have
`cos""(pi)/(11)+cos""(3pi)/(11)+cos""(5pi)/(11)+cos""(7pi)/(11)+cos""(9pi)/(11)`
`=(cos((5pi)/(11)).sin((pi)/(11)+(9pi)/(1))/(2))/(sin((pi)/(11)))`
`=(cos""(5pi)/(11)sin""(5pi)/(11))/(sin""(pi)/(11))=(1)/(2)((10pi)/(11))/(sin((pi)/(1)))=(1)/(2)`
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Knowledge Check

  • (1+"cos"(pi)/8)(1+"cos"(3pi)/8)(1+"cos"(5pi)/8)(1+"cos"(7pi)/8)=

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