If \(\rm \frac{\sin x-\cos x}{\sin x+\cos x}=\frac{2}{5}\), then the value of \(\rm \frac{1+\cot^2x}{1-\cot^2x}\) is:

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SSC CGL 2023 Tier-I Official Paper (Held On: 19 Jul 2023 Shift 1)
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  1. 2.25
  2. 1.45
  3. 3.75
  4. 5.25

Answer (Detailed Solution Below)

Option 2 : 1.45
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Detailed Solution

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Calculation:

\(\rm \frac{\sin x-\cos x}{\sin x+\cos x}=\frac{2}{5}\)

⇒ \(\rm \frac{\sin x+\cos x}{\sin x-\cos x}=\frac{5}{2}\) 

Applying C & D rule, we get

⇒ \(\rm \frac{\sin x}{\cos x}=\frac{5 + 2}{5 -2}\) 

⇒ tan x = 7/3

⇒ cot x = 3/7

Now, the value of

 \(\rm \frac{1+\cot^2x}{1-\cot^2x}\)

⇒ \(\rm \frac{1+(\frac{3}{7})^2}{1-(\frac{3}{7})^2}\) 

⇒ 58/40

⇒ 1.45

∴ The correct answer is 1.45

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