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AP EAMCET2014MathematicsTrigonometric Ratios & Identities

If x and y are acute angles such that x+ y= 3 2 and x+ y= 3 4 , then (x+y) equals to

Options

  1. A2 5
  2. B3 4
  3. C3 5
  4. D4 5

Correct answer

D. 4 5

Step-by-step solution

Given, x+ y= 3 2 2 ( x+y 2 ) ( x-y 2 )= 3 2 and aligned & x+ y= 3 4 & 2 ( x+y 2 ) ( x-y 2 )= 3 4 & 2 ( x+y 2 ) ( x-y 2 ) 2 ( x+y 2 ) ( x-y 2 ) = 3 / 4 3 / 2 & ( x+y 2 )= 1 2 & (x+y)= 2 ( x+y 2 ) 1+ ^2 ( x+y 2 ) & = 2 1 2 1+ ( 1 2 )^2 = 4 4+1 = 4 5 & aligned

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