8 sec² ∅ + 2 cosec² ∅ এর সর্বনিম্ন মান কত?

  1. 14
  2. 16
  3. 18
  4. 20

Answer (Detailed Solution Below)

Option 3 : 18
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Detailed Solution

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8 sec² ∅ + 2 cosec²∅

⇒ 8(1 + tan²∅) + 2(1 + cot²∅)

⇒ 8 + 2 + 8 tan²∅ + 2 cot²∅

 a tan²∅ + b cot²∅ এর সর্বনিম্ন মান = 2√ab 

⇒ 10 + 2√(8 × 2)

⇒ 10 + 2√16 = 18

a sec2θ + b cosec2θ  এর জন্য সর্বনিম্ন মান,

⇒ (√a + √b)2

প্রশ্ন অনুসারে,

⇒ (√8 + √2)2

⇒ 8 + 2 + 2(√8 × 2)
⇒ 10 + 2(√16)
⇒ 10 + 2 × 4
⇒ 18
∴  সর্বনিম্ন মান হল 18
 
a sec2θ + b cosec2θ, এর জন্য, সর্বোচ্চ মান হল অসীম। 
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