Correct Answer - Option 3 : 16/49

**Given :**

Cos^{4 }θ – sin^{4 }θ = 4/7

**Formula used :**

Cos 2θ = 1 – 2 sin^{2 }θ = cos^{2 }θ – sin^{2 }θ

Sin^{2 }θ + cos^{2 }θ = 1

**Calculations :**

Cos^{4 }θ – sin^{4 }θ = 4/7

(cos^{2 }θ + sin^{2 }θ )(Cos^{2 }θ – sin^{2 }θ) = 4/7

Cos^{2 }θ – sin^{2 }θ = 4/7

Now

(1 – 2 sin^{2 }θ) × (cos 2θ) = (cos^{2 }θ – sin^{2 }θ) (cos^{2 }θ – sin^{2 }θ)

⇒ (4/7) × (4/7)

⇒ 16/49

**∴ 16/49 will be the correct answer **