Question

2sin²θ cos²θ - (sin⁴θ + cos⁴θ) = ?
(a) 2
(b) 3
(c) 1
(d) 4​​

Answer 1

Answer:

• Correct Option is (c) 1

Step-by-step explanation:

2Sin²θ Cos²θ - (Sin⁴θ + Cos⁴θ)

➻ 2Sin²θ Cos²θ - { (Sin²θ + Cos²θ)²}

Splitting the term by using (a-b)² = a² + b² -2ab

➻ 2Sin²θ Cos²θ - { (Sin²θ + Cos²θ)²}

➻ 2Sin²θ Cos²θ + { (Sin²θ - Cos²θ)²}

➻ 2Sin²θ Cos²θ + (Sin²θ + Cos²θ - 2SinθCosθ)

➻ 2Sin²θ Cos²θ + Sin²θ + Cos²θ - 2SinθCosθ

➻ Sin²θ + Cos²θ

As we know the identity Sin²θ + Cos²θ = 1

➻ 1

• Hence ,the required answer is 1.

Correct Option is (c) 1