Question

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

Options

• ${\displaystyle \frac{5\pi }{3}}$

• ${\displaystyle \frac{5\pi }{4}}$

• ${\displaystyle \frac{3\pi }{2}}$

• ${\displaystyle \frac{7\pi }{4}}$

Answer 1

The value of θ in (π, 2π) satisfying the equation sin²θ - cos²θ = 1 is ${\displaystyle \underline{\frac{3\pi }{2}}}$.

Explanation:

sin²θ - cos²θ = 1

⇒ cos 2θ = -1

⇒ cos 2θ = cos π

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

⇒ ${\displaystyle \theta =n\pi \pm \frac{\pi }{2}}$

⇒ ${\displaystyle \theta =\frac{3\pi }{2}}$ .............[∵ θ ∈ (π, 2π)]