2 Cot x = 5 எனில், \(\frac{2 \operatorname{Cos} x-\operatorname{Sin} x}{2 \operatorname{Cos} x+\operatorname{Sin} x}\) எதற்குச் சமம்?

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SSC CGL 2023 Tier-I Official Paper (Held On: 19 Jul 2023 Shift 3)
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  1. \(\frac{3}{4}\)
  2. \(\frac{1}{3}\)
  3. \(\frac{5}{6}\)
  4. \(\frac{2}{3}\)

Answer (Detailed Solution Below)

Option 4 : \(\frac{2}{3}\)
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Detailed Solution

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கணக்கீடு :

\(\frac{2 \operatorname{Cos} x-\operatorname{Sin} x}{2 \operatorname{Cos} x+\operatorname{Sin} x}\)

⇒ sinx(2cotx - 1)/sinx(2cotx + 1)

⇒ (2cotx - 1)/(2cotx + 1)

⇒ (2 x 5/2 - 1)/(2 x 5/2 + 1)

⇒ (5 - 1)/(5 + 1)

⇒ 4/6 = 2/3

∴ சரியான பதில் 2/3.

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