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      Question

      If sin 2  A + sin 4  A = 1 and cos

      2  A + cos 4  A = 1, then find the value of (sin 4  A - cos 4  A)
      A (cos A + sin A) (cos A - sin A) Correct Answer Incorrect Answer
      B 1 Correct Answer Incorrect Answer
      D (sin A + cos A) (sin A - cos A) Correct Answer Incorrect Answer

      Solution

      sin 2  A + sin 4  A = 1 -------- (I)
      cos 2  A + cos 4  A = 1 ------- (II)
      On subtracting equation I from II,
      We get, sin 2  A + sin 4  A - cos 2  A - cos 4  A = 1 - 1
      Or, sin 4  A - cos 4  A = cos 2  A - sin 2  A
      Or, sin 4  A - cos 4  A = (cos A + sin A) (cos A - sin A)

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