Double or Half Angle Formula

Question

Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.)

cos(2θ) + sin²(θ) = 0

Answer 1

You might want to use your double angle identities. You know that cos(2θ) = 1 - 2sin²(θ). Therefore you can plug it in in your original equation.

cos(2θ) + sin²(θ) = 0

1 - 2sin²(θ) + sin²(θ) = 0 Double angle identity

1 - sin²(θ) = 0 Symplification

cos²(θ) = 0 Phytagorean identity

cos(θ) = 0 Square root both sides

θ = π/2 , 3π/2