Question
Download Solution PDFयदि cosec A - cot A = \(\frac{1}{4}\) है, तो tan A का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
cosec A - cot A = \(\frac{1}{4}\)
प्रयुक्त अवधारणा:
1. cosec2 A - cot2 A = 1
2. cot A = 1 ÷ tan A
गणना:
cosec A - cot A = \(\frac{1}{4}\) ....(1)
अवधारणा के अनुसार,
cosec2 A - cot2 A = 1
⇒ (cosec A + cot A)(cosec A - cot A) = 1
⇒ (cosec A + cot A) × \(\frac{1}{4}\) = 1
⇒ (cosec A + cot A) = 4 ....(2)
अब, समीकरण (2) - समीकरण (1),
2cot A = 4 - 1/4
⇒ cot A = 15/8
⇒ tan A = 8/15
∴ tan A का अभीष्ट मान \(\frac{8}{15}\) है।
Last updated on Jul 21, 2025
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