Question
Download Solution PDF9cosA + 12sinA = 15 எனில், cotA இன் மதிப்பைக் கண்டுபிடி.
A. 3/4
B. 12/13
C. 1/3
D. 3/5
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFகொடுக்கப்பட்டது:
9cosA + 12sinA = 15
பயன்படுத்தப்பட்ட சூத்திரம்:
(a + b)2 = a2 + b2 + 2ab
CosecA = 1/SinA
Cot2A = (Cosec2A - 1)
கணக்கீடு:
9cosA+12sinA=15
இருபுறமும் 3 ஆல் வகுக்கவும்,
3cos A + 12 sin A = 5
இருபுறமும் SinA ஆல் வகுக்கவும்,
3cosA/sinA + 4sinA/sinA = 5/sinA
⇒ 3cotA + 4 = 5 cosec A
இருபுறமும் வர்க்கப்படுத்தவும்
(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 இன் இறுதி மதிப்பு 3/4.
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