Question

Solve ${sin}^{3}\theta\:cos\theta- {cos}^{3}\theta\:sin\theta=\frac{1}{4}$​

Answer 1

Solution :

Given, sin³θ cosθ - cos³θ sinθ = 1/4

⇒ sinθ cosθ (sin²θ - cos²θ) = 1/4

⇒ (2 sinθ cosθ) (- cos2θ) = 2

⇒ 2 sin2θ cos2θ = - 1

⇒ sin4θ = - 1

⇒ 4θ = (4n - 1) . π/2 , n ∈ ℤ

∴ θ = (4n - 1) . π/8 , n ∈ ℤ

Rules :

• 2 sinθ cosθ = sin2θ

• cos²θ - sin²θ = cos2θ