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KCET2013MathematicsTrigonometric Ratios & Identities

If x- y= 1 2 and x- y=1 , then (x+y) is equal to

Options

  1. A3 8
  2. B- 3 8
  3. C4 3
  4. D- 4 3

Correct answer

C. 4 3

Step-by-step solution

Given, x- y= 1 2 ...(i) and x- y=1...(ii) 2 x+y 2 x-y 2 = 1 2 ...(iii) and -2 x+y 2 x-y 2 =1...(iv) On dividing Eq. (iv) by Eq. (iii), we get gathered - ( x+y 2 )=2 ( x+y 2 )=-2 (v) Now, (x+y)= 2 ( x+y 2 ) 1- ² ( x+y 2 ) gathered ( 2 = 2 1- ² )= 2(-2) 1-(-2)² [using Eq. (v)] = -4 1-4 = -4 -3 = 4 3

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