Correct Answer - Option 3 : 16/49
Given :
Cos4 θ – sin4 θ = 4/7
Formula used :
Cos 2θ = 1 – 2 sin2 θ = cos2 θ – sin2 θ
Sin2 θ + cos2 θ = 1
Calculations :
Cos4 θ – sin4 θ = 4/7
(cos2 θ + sin2 θ )(Cos2 θ – sin2 θ) = 4/7
Cos2 θ – sin2 θ = 4/7
Now
(1 – 2 sin2 θ) × (cos 2θ) = (cos2 θ – sin2 θ) (cos2 θ – sin2 θ)
⇒ (4/7) × (4/7)
⇒ 16/49
∴ 16/49 will be the correct answer