Question

Cos⁴θ – sin⁴θ = 4/7 then find the value of (1 – 2sin²θ) × (cos2θ)

1. 1/7
2. 25/49
3. 16/49
4. 0 

Answer 1

Correct Answer - Option 3 : 16/49

Given :

Cos⁴θ – sin⁴θ = 4/7

Formula used :

Cos2θ = 1 – 2sin²θ = cos²θ – sin²θ

Sin²θ + cos²θ = 1

Calculations :

Cos⁴θ – sin⁴θ = 4/7

(cos²θ + sin²θ )(Cos²θ – sin²θ) = 4/7

Cos²θ – sin²θ = 4/7

Now

(1 – 2sin²θ) × (cos2θ) = (cos²θ – sin²θ) (cos²θ – sin²θ)

⇒ (4/7) × (4/7)

⇒ 16/49

∴ 16/49 will be the correct answer