Question
Download Solution PDFएक त्रिभुज ABC में, sec A (sin B cos C + cos B sin C) बराबर होगा:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
- sin (A + B) = sin A cos B + cos A sin B ___(1)
- त्रिभुज के तीनों कोणों का योग 180° होता है
- sin(180 - θ) = sin θ ___(2)
गणना:
त्रिभुज ABC में, कोणों का योग = A + B + C = 180°
⇒ B + C = 180 - A ___(3)
दिया गया है , sec A (sin B cos C + cos B sin C)
⇒ sec A sin (B + C) ∵ {(1) का उपयोग करने पर}
⇒ sec A. sin (180 - A) ∵ {(2) का उपयोग करने पर}
⇒ sec A. sin A ∵ {(3) का उपयोग करने पर}
⇒ \({\sin A \over \cos A }\)
⇒ tan A
∴ सही उत्तर विकल्प (3) है।
Last updated on May 26, 2025
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