Question
Download Solution PDFयदि 9cosA + 12sinA = 15 है, तो cotA का मान ज्ञात कीजिए।
A. 3/4
B. 12/13
C. 1/3
D. 3/5
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया है:
9cosA + 12sinA = 15
प्रयुक्त सूत्र:
(a + b)2 = a2 + b2 + 2ab
CosecA = 1/SinA
Cot2A = (Cosec2A – 1)
गणना:
9cosA + 12sinA = 15
दोनों ओर 3 से भाग करने पर,
3cos A + 12 sin A = 5
दोनों ओर SinA से भाग करने पर,
3cosA/sinA + 4sinA/sinA = 5/sinA
⇒ 3cotA + 4 = 5 cosec A
दोनों ओर वर्ग करने पर,
(3cotA + 4)2 = (5cosecA)2
⇒ 9cot2A + 16 + 24cotA = 25cosec2 A
⇒ 9cot2A + 16 + 24cotA = 25(cot2A + 1)
⇒ 9cot2A + 16 + 24cotA = 25cot2A + 25
⇒ 16cot2A – 24cotA + 9 = 0
⇒ (4cot A – 3)2 = 0
⇒ 4cotA – 3 = 0
⇒ 4cotA – 3 = 0
⇒ cotA = 3/4
∴ cotA का अंतिम मान 3/4 है।
Last updated on Jul 10, 2025
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