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      Question

      If sin(x + y) = 1 and sin(x - y) = (1/2), then what is

      the value of sinx cosx + 2sin2y + cos2y? 
      A {(√3 + 5)/4} Correct Answer Incorrect Answer
      B {(√3 + 3)/4} Correct Answer Incorrect Answer
      C 3/5 Correct Answer Incorrect Answer
      D {(√2 + 5)/4} Correct Answer Incorrect Answer

      Solution

      We have given, sin(x + y) = 1 and sin(x - y) = 1/2 So, sin(x + y) = 1 Or, sin(x + y) = sin90° Or, (x + y) = 90° ......(i) Again, sin(x - y) = 1/2 Or, sin(x - y) = sin30° Or, (x - y) = 30° ......(ii) By adding (i) and (ii) we get, 2x = 120° Or, x = 60° Putting the value of 'x' in the eq (i) we get, y = 30° Now, sinx cosx + 2sin2y + cos2y = sin60° X cos60° + 2 X sin230° + cos230° = = (1/2) X (√3/2) + 2 X (1/2)2 + (√3/2)2 = (1/2) X (√3/2) + 2 X (1/4) + (3/4) = (√3/4) + (1/2) + (3/4) = {(√3 + 2 + 3)/4} = {(√3 + 5)/4} 

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