Question
Download Solution PDFযদি 9cosA + 12sinA = 15 হয়, তাহলে cotA এর মান নির্ণয় করো।
A. 3/4
B. 12/13
C. 1/3
D. 3/5
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFপ্রদত্ত:
9cosA + 12sinA = 15
ব্যবহৃত সূত্র:
(a + b)2 = a2 + b2 + 2ab
CosecA = 1/SinA
Cot2A = (Cosec2A - 1)
গণনা:
9cosA+12sinA=15
উভয় পক্ষে 3 দিয়ে ভাগ করলে,
3cos A + 12 sin A = 5
উভয় পক্ষে SinA দিয়ে ভাগ করলে,
3cosA/sinA + 4sinA/sinA = 5/sinA
⇒ 3cotA + 4 = 5 cosec A
উভয় পক্ষে বর্গ করলে
(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 এর চূড়ান্ত মান হল 3/4.
Last updated on Jul 1, 2025
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