यदि sec θ + cos θ = 32 है, तब sec2 θ+ cos2 θ का मान कितना है?

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SSC CGL 2023 Tier-I Official Paper (Held On: 14 Jul 2023 Shift 4)
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  1. 1000
  2. 1022
  3. 1024
  4. 1020

Answer (Detailed Solution Below)

Option 2 : 1022
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प्रयुक्त सूत्र:

(a + b)2 = a2 + b2 + 2ab

गणना

sec θ + cos θ = 32

दोनों पक्षों का वर्ग करने पर:

(sec θ + cos θ)2 = sec2 θ+ cos2 θ + 2 sec θ cos θ

⇒ 1024 - 2 = sec2 θ+ cos2 θ 

⇒ sec2 θ+ cos2 θ = 1022

समीकरण का मान 1022 है। 

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