In the interval - π 2 , π 2 , the equation log sin ⁡ θ ⁡ cos ⁡ 2 θ = 2 has

Step-by-step solution

Since, - π 2 ≤ θ ≤ π 2 ⇒ sin ⁡ θ ∈ - 1 , 1 Here sin ⁡ θ ∈ 0 , 1 for log sin ⁡ θ ⁡ cos ⁡ 2 θ = 2 to be defined. ⇒ cos ⁡ 2 θ = sin 2 ⁡ θ ⇒ 1 - 2 sin 2 ⁡ θ = sin 2 ⁡ θ ⇒ sin 2 ⁡ θ = 1 3 ⇒ sin ⁡ θ = 1 3 (as sin ⁡ θ ∈ 0 , 1 ) ⇒ The equation has a unique solution.