Question

Let f(θ) = sin θ (sin θ + sin 3θ) then ______.

विकल्प

• f(θ) ≥ 0 ∀ θ ∈ R

• f(θ) ≤ 0 ∀ θ ∈ R

• f(θ) ≥ 1 ∀ θ ∈ R

• f(θ) ≤ 1 ∀ θ ∈ R

Answer 1

Let f(θ) = sin θ (sin θ + sin 3θ) then f(θ) ≥ 0 ∀ θ ∈ R.

Explanation:

f(θ) = sin θ (sin θ + sin 3θ)

= sin θ (2 sin 2 θ cosθ)

= (2 sin θ cos θ) sin 2θ

= (sin 2θ)² ≥ 0 ∀ θ ∈ R