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COS10*COS30*COS60*COS70=(3/16) SOLVE IT HOW TO SOLVETHIS QUESTION

COS10*COS30*COS60*COS70=(3/16) SOLVE IT HOW TO SOLVETHIS QUESTION
 

Grade:12th pass

2 Answers

Himanshu
103 Points
5 years ago
Your question is definitely wrong. It must be as follows:-
cos10.cos30.cos50.cos70 = 3/16
L.H.S. = cos30.cos10.cos50.cos70
  = root(3)/2 × cos10.cos50.cos70
  = root(3)/4 × (cos60 + cos40)cos70
  = root(3)/8 × 2cos60.cos70 + 2cos40.cos70
  = root(3)/8 × (cos70 + cos110 + cos30)
  = root(3)/8 × (cos70 - cos70 + root(3)/2)
  = [root(3) × root(3)] / (8×2)
  = 3/16 = R.H.S.
Hence, proved.
Kushagra Madhukar
askIITians Faculty 629 Points
10 months ago
Dear student,
Please find the solution to your problem below.
 
The question seems wrong as the answer for the said question would be different around 2.33/16, you can check it by calculator.
Coming back to the the question it might actually be
 
cos10.cos30.cos50.cos70 = 3/16
L.H.S. = cos30.cos10.cos50.cos70
  = root(3)/2 × cos10.cos50.cos70
  = root(3)/4 × (cos60 + cos40)cos70
  = root(3)/8 × 2cos60.cos70 + 2cos40.cos70
  = root(3)/8 × (cos70 + cos110 + cos30)
  = root(3)/8 × (cos70 - cos70 + root(3)/2)
  = [root(3) × root(3)] / (8×2)
  = 3/16 = R.H.S.
Hence, proved.
 
Hope it helps.
Thanks and regards,
Kushagra

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