Find The Value of Given Term ?

The value of sin²5º + sin² 10º + sin² 15º + sin² 20º + ……. Sin² 90º is

  1. 7
  2. 8
  3. 9
  4. 19/2
Anurag Mishra Professor Asked on 1st October 2015 in Maths.
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1 Answer(s)

Answer : (4) 19/2

Explanation:-

Sin2 5o + sin2 85o = Sin2 5o + Sin2 (90 – 5)o
= Sin2 5o + Cos2 5o = 1
Similarly, sin2 10o + sin2 80o = 1
sin2 15o + sin2 75o = 1
sin2 20o + sin2 70o = 1
sin2 25o + sin2 65o = 1
sin2 30o + sin2 60o = 1
sin2 35o + sin2 55o = 1
sin2 40o + sin2 50o = 1
sin2 45o = 1/2
sin2 90o = 1

Then, the sum of sin2 5o + sin2 10o + sin2 15o +………….+sin2 90o  = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1/2  + 1
= 9 + 1/2
= (18 + 1)/2
= 19/2
Hence, the answer is (4) 19/2

Anurag Mishra Professor Answered on 3rd October 2015.
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