The value of the expression

Sin²1º + Sin²11º+Sin²21º+Sin²31º+Sin²41º+Sin²45º+Sin²49º+Sin²59º+Sin²69º+Sin²79º+Sin²89º is:

  1. 5
  2. 5 ½
  3. 0
  4. 4 ½
Anurag Mishra Professor Asked on 10th December 2015 in Maths.
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  • 1 Answer(s)

    Answer:  (2) 5  1/2

    Sin210 + Sin2110 + Sin2210 + Sin231o + Sin241o + Sin245o + Sin245o + Sin249o + Sin259o + Sin269o + Sin279o + Sin289o

     = Sin21o + Sin2110 + Sin2210 + Sin231o + Sin241o + Sin245o + Sin245o + Sin2(90 – 41)o + Sin2(90 – 31)o + Sin2(90 – 21)o + Sin2(90 – 11)o + Sin2(90 – 1)o
     = Sin21o + Sin2110 + Sin2210 + Sin231o + Sin241o + Sin245o + Sin245o + Cos241o + Cos231o + Cos2210 + Cos211o + Cos21o
     = Sin21o + Cos21o +  Sin2110 + Cos211o + Sin2210 + Cos2210 + Sin231o + Cos231o + Sin241o + Cos241o + Sin245o
    As we know that Sin2A + Cos2A = 1
    Then, 1 + 1 + 1 + 1 + 1 + ½
     = 5 + 1/2
    = 5  1/2

    Hence, the correct answer is option (2) 5  1/2. 

    Anurag Mishra Professor Answered on 10th December 2015.
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