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text  If  end text f left parenthesis x right parenthesis equals fraction numerator cos squared x plus sin to the power of 4 x over denominator sin squared x plus cos to the power of 4 x end fraction text   for x∈R end text then f(2002) =

  1. 1
  2. 2
  3. 3
  4. 4

The correct answer is: 1


    open parentheses cos squared x plus sin to the power of 4 x close parentheses minus open parentheses sin squared x plus cos to the power of 4 x close parentheses
equals open parentheses cos squared x minus sin squared x close parentheses minus open parentheses cos to the power of 4 x minus sin to the power of 4 x close parentheses
equals cos 2 x minus cos 2 x equals 0
not stretchy rightwards double arrow f left parenthesis x right parenthesis equals fraction numerator cos squared x plus sin to the power of 4 x over denominator sin squared x plus cos to the power of 4 x end fraction equals 1

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