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sashaice [31]
3 years ago
10

1. find the exact value of cos2θ if sin 2θ=3/4 and θ is between 0° and 90°

Mathematics
1 answer:
musickatia [10]3 years ago
5 0

Answer:

<u>Identities used:</u>

  • sin²θ + cos²θ = 1
  • cos2θ = cos²θ - sin²θ

#1

  • sin2θ = 3/4, and θ in the first quadrant
  • cos²2θ = 1 - sin²2θ
  • cos2θ = √(1 - sin²2θ) = √(1 - 9/16) = √(7/16) = √7 / 4

#2

  • sinθ(cos²θ - cos2θ) =
  • sinθ(cos²θ - (cos²θ - sin²θ) =
  • sinθ(sin²θ) =
  • sin³θ

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