Question

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

2. verify that sinθ(cos²θ-cos2θ)=sin³θ

Answer 1

Identities used:

• 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