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AP EAMCET201923 Apr 2019Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

(a, b, c ) are the sides of a scalene triangle (A B C ). If angles ( , , ) lie between 0 and ( ) such that ( = a b+c , = b c+a ) and ( = c a+b ), then ( ^2 2 + ^2 2 + ^2 2 = )

Options

  1. A( 1 3 )
  2. B2
  3. C1
  4. D( 3 2 )

Correct answer

C. 1

Step-by-step solution

It is given ( = a b+c ) ( 1- ^2 2 1+ ^2 2 = a b+c ) On applying componendo and dividendo law, we get ( 2 ^2 / 2 2 = b+c-a b+c+a ) ( ^2 / 2= b+c-a a+b+c ) Similarly, ( ^2 2 = c+a-b a+b+c ) and ( ^2 2 = a+b-c a+b+c ) So, ( ^2 2 + ^2 2 + ^2 2 = a+b+c a+b+c =1 ) Hence, option (c) is correct.

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