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2 years ago

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

Mathematics

1 answer:

musickatia [10]2 years ago

5 0

Answer:

Identities used:

sin²θ + cos²θ = 1
cos2θ = cos²θ - sin²θ

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

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

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