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The value of cos 180/11+ cos 3*180/11+cos 5*180/11+cos 7*180/11+cos 9*180/11 is

  1. 0
  2. -1/2
  3. 1/2
  4. 1

Abhipsa Sadangi , 15 Years ago
Grade 11
anser 2 Answers
suryakanth AskiitiansExpert-IITB

Dear abhipsa,

we know that

cos a + cos 3a + cos 5a + .. + cos(2n-1)a = sin 2na/2 sin a

In our case n = 5

therefore RHS = sin 10a / (2sina)

=>RHS =  sin 2*5 *(180/11) / 2sin (180/11)

=> RHS = sin (180/11) /2 sin(180/11)

=> rhs = 1/2

hence the answer is option 3 ......1/2

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