যদি acot θ = b হয়, তাহলে \(\frac{bcosθ - asinθ}{bcosθ + asinθ}\) এর মান কত হবে?

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SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 4)
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  1. \(\frac{b^2 + a^2}{b^2 - a^2}\)
  2. b2 + a2
  3. \(\frac{b^2 - a^2}{b^2 + a^2}\)
  4. 0

Answer (Detailed Solution Below)

Option 3 : \(\frac{b^2 - a^2}{b^2 + a^2}\)
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Detailed Solution

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প্রদত্ত:

a cot θ = b

গণনা:

\(\frac{bcosθ - asinθ}{bcosθ + asinθ}\)

পুরো সমীকরণটিকে cos θ দ্বারা ভাগ করে পাই:

⇒ (b - asinθ/cosθ)/(b + asinθ/cosθ)

⇒ (b - atanθ)/(b + atanθ)

⇒ (b - a × a/b)/(b + a × a/b) 

⇒ (b2 - a2)/(b2 + a2

সুতরাং, রাশিটির মান হল (b2 - a2)/(b2 + a2)

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