sinθ के पदों में sin4θ + cos4θ को कैसे लिखा जा सकता है?

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SSC CGL 2022 Tier-I Official Paper (Held On : 03 Dec 2022 Shift 2)
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  1. 2sin4θ + 2sin2θ  - 1
  2. 2sin4θ - 2sin2θ 
  3. 2sin 4 θ - 2sin 2 θ - 1
  4. 2sin4θ - 2sin2θ + 1

Answer (Detailed Solution Below)

Option 4 : 2sin4θ - 2sin2θ + 1
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SSC CGL Tier 1 2025 Full Test - 01
100 Qs. 200 Marks 60 Mins

Detailed Solution

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दिया गया है:

sin4θ + cos4θ

प्रयुक्त अवधारणा:

cos2θ = 1 - sin2θ

गणना:

sin4θ + cos4θ

⇒ sin4θ + (cos2θ)2

⇒ sin4θ + (1 - sin2θ)2

⇒ sin4θ + 1 + sin4θ - 2sin2θ

⇒ 2sin4θ + 1 - 2sin2θ

⇒ 2sin4θ - 2sin2θ + 1

∴ अभीष्ट उत्तर 2sin4θ - 2sin2θ + 1 है।

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