Question
Download Solution PDFcosec
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFप्रयुक्त संकल्पना:
Cosec 45° = √2 ; sec 45° = √2
Cosec 30° = 2 ; sec 30° = (2/√3)
गणना:
Cosec 75° = cosec (45 + 30)
cosec (45 + 30) = (sec 45 × sec 30 × cosec 45 × cosec 30)/{(sec 45 × cosec 30) + (cosec 45 × sec 30)}
⇒ (√2 × (2/√3) × √2 × 2)/{(√2 × 2) + (√2 × (2/√3))}
⇒ (8/√3)/{2√2 + (2√2/√3)}
⇒ (8/√3)/{(2√6 + 2√2)/√3}
⇒ 8/(2√6 + 2√2)
पद का प्रमेयीकरण करके,
⇒ 8 × (2√6 - 2√2)/{(2√6 + 2√2) × (2√6 - 2√2)}
⇒ (16√6 - 16√2)/{(2√6)2 - (2√2)2}
⇒ 16 × (√6 - √2)/{24 - 8}
⇒ 16 × (√6 - √2)/16 = (√6 - √2)
∴ सही उत्तर (√6 - √2) है।
Last updated on Jul 14, 2025
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