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If sin 4 x + sin 2 x = 1, then the value of cos 2 x + cos 4 x is 1 – 2cos 6 x 1 – 2sin 6 x 1 0

If sin4x + sin2x = 1, then the value of cos2x + cos4x is
  1. 1 – 2cos6x
  2. 1 – 2sin6x
  3. 1
  4. 0

Grade:11

2 Answers

SJ
askIITians Faculty 97 Points
one year ago
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Parth Parekh
27 Points
8 months ago
    sin4x+sin2x=1
so,sin2x(sin2x+1)=1
     1-cos2x(1-cos2x+1)=1
     cos2x(-1+cos2x-1)=1-1
     cos2x(cos2x-2)=0
    
    cos2x=0   (or)   cos2x-2=0 
 
    cosx=0     (or)   cosx=\sqrt{2}\approx 1.41 , but it is not possible
                            because,range of cos=[-1,1]
 
  cos2x + cos4x= (cosx)2+(cosx)4
                          = (0)2+(0)4
                               = 0 
 
so,the answer will be zero.
 
 
                               

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