Question
Download Solution PDF64 tan2θ + 81 cosec2θ + 76 యొక్క కనిష్ఠ విలువను కనుగొనండి.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFఉపయోగించిన 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.
Last updated on Jun 26, 2025
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