Question
Download Solution PDFयदि sec A + tan A = 5 है, तब sin A बराबर है:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
sec A + tan A = 5
प्रयुक्त संकल्पना:
यदि sec A + tan A = x तब,
⇒ sec A - tan A = 1/x
प्रयुक्त सूत्र:
Sin θ = P/H ; sec θ = H/B ; tan θ = P/B
पाइथागोरस प्रमेय:
H2 = P2 + B2
जहाँ, H = कर्ण ; P = लंब ; B = आधार
गणना:
⇒ sec A + tan A = 5 ------- (1)
तब,
⇒ sec A - tan A = 1/5 -------- (2)
समीकरण (1) और (2) जोड़ने पर
⇒ Sec A + tan A + sec A - tan A = 5 + (1/5)
⇒ 2 × sec A = 26/5
⇒ sec A = 13/5 = H/B
पाइथागोरस प्रमेय द्वारा:
⇒ H2 = P2 + B2
⇒ (13)2 = P2 + 52
⇒ P2 = 169 - 25 = 144
⇒ P = √144 = 12
Sin A = P/H = 12/13
∴ सही उत्तर 12/13 है।
Last updated on Jun 13, 2025
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