If sec x – cos x = 4, then what will be the value of ?

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SSC CGL 2022 Tier-I Official Paper (Held On : 08 Dec 2022 Shift 3)
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  1. 9/4
  2. 1/4

Answer (Detailed Solution Below)

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SSC CGL Tier 1 2025 Full Test - 01
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Detailed Solution

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Given:

sec x – cos x = 4

Concept Used:

Cos x = 

Calculation:

Let cos x = m 

⇒ sec x – cos x = 4

⇒   - cos x = 4

⇒  - m = 4

⇒ 1 - m= 4m

⇒ m+ 4m -1 = 0

Finding roots of the above equation:

⇒ m =  

⇒ m = 

⇒ m =  - 2

Finding the value:

⇒ 

Putting the value of m in above equation:

⇒  

⇒ √5 + 2 + √5 - 2 = 

Hence, the value of   is  .

Shortcut Trick 

We know, if x - 1/x = a then x + 1/x = √(a2 + 4)

 = secx + cos x = sec x + 1/sec x

Here, similarly sec x - 1/sec x = 4, then sec x + 1/sec x = √(42 + 4) = √20 = 2√5

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