MathematicsIf sinA+ sin 2 A =1,   then which of the following is the value of the expression cos 2 A+ cos 4 A  ?

If sinA+ sin 2 A =1,   then which of the following is the value of the expression cos 2 A+ cos 4 A  ?


  1. A
    1
  2. B
    1 2  
  3. C
    2
  4. D
    3 

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    Solution:

    The given equation is,
    sinA+ sin 2 A=1 sinA=1 sin 2 A   Apply the following:
    1 sin 2 A= cos 2 A  
    Therefore,
    sinA= cos 2 A sin 2 A= cos 4 A   We have,
    cos 2 A+ cos 4 A=sinA+ sin 2 A cos 2 A+ cos 4 A=1  
    Therefore, the value of the expression cos 2 A+ cos 4 A =1.  
    Hence, option (1) is correct.
     
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