Question
Download Solution PDFजर 9cosA + 12sinA = 15 असेल, तर cotA चे मूल्य शोधा.
A. 3/4
B. 12/13
C. 1/3
D. 3/5
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेले आहे:
9cosA + 12sinA = 15
वापरलेले सूत्र:
(a + b)2 = a2 + b2 + 2ab
CosecA = 1/SinA
Cot2A = (Cosec2A - 1)
गणना:
9cosA+12sinA=15
दोन्ही बाजूंस 3 ने भाग देवू,
3cos A + 12 sin A = 5
दोन्ही बाजूंस SinA ने भाग देवू,
3cosA/sinA + 4sinA/sinA = 5/sinA
⇒ 3cotA + 4 = 5 cosec A
दोन्ही बाजूंचा वर्ग केल्यास,
(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 चे अंतिम मूल्य 3/4 असेल.
Last updated on Jun 27, 2025
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