If \(\rm \frac{21\ cosA+3\ sinA}{3\ cosA+4\ sinA}\) = 2, then find the value of cot A

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SSC CGL 2023 Tier-I Official Paper (Held On: 26 Jul 2023 Shift 2)
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  1. \(\frac{9}{11}\)
  2. \(\frac{11}{9}\)
  3. \(\frac{1}{3}\)
  4. \(\frac{11}{10}\)

Answer (Detailed Solution Below)

Option 3 : \(\frac{1}{3}\)
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Detailed Solution

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Concept used:

Cosθ/ Sinθ = Cotθ

Calculation:

\(\rm \frac{21\ cosA+3\ sinA}{3\ cosA+4\ sinA}\) = 2

By dividing by Sin A we get

⇒ (21 cot A + 3) / (3 cot A + 4) = 2

⇒ 15 cot A = 5

cot A = 1/3

∴ The correct option is 3

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