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যদি  = A sinx + B cosx + C হয়, যেখানে 0 , তবে নীচের কোনটি সঠিক?

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  1. A + B = 0
  2. A + B - 2 = 0
  3. A + B + 2 = 0
  4. A + B - 1 = 0

Answer (Detailed Solution Below)

Option 2 : A + B - 2 = 0
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Detailed Solution

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ধারণা:

sin2x + cos2x = 1

গণনা:

আমরা জানি  = A sinx + B cosx + C

⇒  = A sinx + B cosx + C

⇒  = A sinx + B cosx + C

⇒  = A sinx + B cosx + C     ----(i)

যদি 0  হয়, তবে sinx

⇒ |sinx - cosx| = -sinx + cosx    -----(ii)

এখন (i) ও (ii) থেকে আমরা পাই 

⇒  = A sinx + B cosx + C

⇒ cosx + sinx + C = A sinx + B cosx + C

A = 1, B = 1 এবং C = 0 তুলনা করে পাই

সুতরাং, A + B - 2 = 0 সঠিক।

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