If \(\rm cos x + sec x = {7 \over2 \sqrt3}\), then the value of cos2x + sec2x will be ________.

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SSC CGL 2023 Tier-I Official Paper (Held On: 26 Jul 2023 Shift 3)
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  1. \(15 \over 12\)
  2. \(10 \over 12\)
  3. \(25 \over 10\)
  4. \(25 \over 12\)

Answer (Detailed Solution Below)

Option 4 : \(25 \over 12\)
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Detailed Solution

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Given:

\(\rm cos x + sec x = {7 \over2 √3}\)

Concept used:

Secx = 1/Cosx

Calculation:

Let cosx = a , then secx = 1/a

As per the question,

⇒ a + 1/a = 7/2√3

⇒ a2 + 1/a2 = (7/2√3)2 - 2

⇒ a2 + 1/a2 = 25 /12

∴ The correct option is 4

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