If x is a real quantity, what is the minimum value of (25 cos2 x + 9 sec2 x)?

This question was previously asked in
SSC CGL 2020 Tier-I Official Paper 16 (Held On : 23 Aug 2021 Shift 1)
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  1. 30
  2. 15
  3. 20
  4. 40

Answer (Detailed Solution Below)

Option 1 : 30
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Detailed Solution

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Given:

(25 cos2 x + 9 sec2 x)

Formula used:

Minimum value of acos2x + bsec2x = 2√ab

Calculation:

According to the question:

Minimum value of acos2x + bsec2x = 2√ab

⇒ 2√(25 × 9)

⇒ (2 × 5 × 3)

⇒ 30

∴ The required value is 30.

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