Question
Download Solution PDFIf 9cosA + 12sinA = 15, find the value of cotA.
A. 3/4
B. 12/13
C. 1/3
D. 3/5
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
9cosA + 12sinA = 15
Formula used:
(a + b)2 = a2 + b2 + 2ab
CosecA = 1/SinA
Cot2A = (Cosec2A – 1)
Calculation:
9cosA+12sinA=15
Divide 3 on both the sides,
3cos A + 12 sin A = 5
Divide SinA on both the sides,
3cosA/sinA + 4sinA/sinA = 5/sinA
⇒ 3cotA + 4 = 5 cosec A
Squaring on both the sides
(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
∴ The final value of cotA is 3/4.
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