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If  = A sinx + B cosx + C, where 0 < x < , then which one of the following is correct?

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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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Concept:

sin2x + cos2x = 1

Calculation:

We have  = A sinx + B cosx + C

⇒  = A sinx + B cosx + C

⇒  = A sinx + B cosx + C

⇒  = A sinx + B cosx + C     ----(i)

If 0 < x < , then sinx < cosx

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

Now from (i) and (ii), we get 

⇒  = A sinx + B cosx + C

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

On comparing A = 1, B = 1 and C = 0

Hence, A + B - 2 = 0 is correct.

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