64 tan2θ + 81 cosec2θ + 76 యొక్క కనిష్ఠ విలువను కనుగొనండి.

  1. 101
  2. 201
  3. 301
  4. 401

Answer (Detailed Solution Below)

Option 3 : 301
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Detailed Solution

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ఉపయోగించిన సూత్రం :

1 + tan2θ = sec2θ

asec2θ + bcosec2θ యొక్క కనిష్ఠ విలువ (√a + √b)2

గణనలు :

64 tan2θ + 81 cosec2θ + 76 = 64 tan2θ + 81 cosec2θ + 64 + 12

⇒ 64 + 64 tan2θ + 81 cosec2θ + 12

⇒ 64(1 + tan2θ) + 81 cosec2θ + 12

⇒ 64 sec2θ + 81 cosec2θ + 12

64 sec2θ + 81 cosec2θ యొక్క కనిష్ఠ విలువ = (√64 + √81)2

⇒ (8 + 9)2

⇒ 289

ఇప్పుడు,

64 sec2θ + 81 cosec2θ + 12 యొక్క కనిష్ఠ విలువ = 289 + 12

⇒ 301

కాబట్టి, 64 tan2θ + 81 cosec2θ + 76 యొక్క కనిష్ఠ విలువ 301.

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