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

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SSC CGL 2022 Tier-I Official Paper (Held On : 12 Dec 2022 Shift 3)
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  1. 4
  2. 2
  3. 1
  4. 0

Answer (Detailed Solution Below)

Option 2 : 2
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SSC CGL Tier 1 2025 Full Test - 01
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Detailed Solution

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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.

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