If 2 sinθ + 2 sin²θ = 2, then the value of 2 cos⁴θ + 2 cos²θ is:

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 12 Dec 2022 Shift 3)

Answer 1

Given:

2 sinθ + 2 sin2θ = 2

Concept used:

sin2 θ + cos2 θ = 1

Calculation:

2 sinθ + 2 sin2θ = 2

⇒ sinθ + sin2θ = 1

⇒ sin θ + 1 - cos2 θ = 1

⇒ sin θ = cos2 θ

⇒ cos4 θ = sin2 θ

So,

2 cos4θ + 2 cos2θ = 2 sin2 θ + 2 sin θ

⇒ 2

∴ The required answer is 2.