Simplify 3(sin4θ + cos4θ) - 2(sin6θ + cos6θ)


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Answer:

1

Step by Step Explanation:
  1. = 3 (sin4θ + cos4θ) - 2 [ (sin2θ)3 + (cos2θ)3]
  2. = 3 (sin4θ + cos4θ) - 2 [ (sin2θ + cos2θ) {(sin2θ)2 + (cos2θ)2 - sin2θ cos2θ } ]
  3. Since sin2θ + cos2θ = 1
    =3 (sin4θ + cos4θ) - 2 {sin4θ + cos4θ - sin2θ cos2θ }
  4. = sin4θ + cos4θ + 2 sin2θ cos2θ
  5. = (sin2θ + cos2θ)2 = 12 = 1

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