Question

The value of θ in (π, 2π) satisfying the equation sin²θ - cos²θ = 1 is ______ 

Options

• `(5pi)/3`

• `(5pi)/4`

• `(3pi)/2`

• `(7pi)/4`

Answer 1

The value of θ in (π, 2π) satisfying the equation sin²θ - cos²θ = 1 is `underline((3pi)/2)`.

Explanation:

sin²θ - cos²θ = 1

⇒ cos 2θ = -1

⇒ cos 2θ = cos π

⇒ 20 = 2nπ ± π ..........[∵ cos θ = cos α ⇒ θ = 2nπ ± α]

⇒ `theta = npi ± π/2`

⇒ `theta = (3pi)/2` .............[∵ θ ∈ (π, 2π)]