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AP EAMCET202017 Sep 2020Morning ShiftMathematicsProperties of TrianglesActual

Let (a, b ) and (c ) be the lengths of the sides of a triangle with its opposite angles (A, B ) and (C ) respectively. If ( C=60^ ), then the value of ( c(a+b)+ (a^2+b^2 ) (b+c)(c+a) ) is

Options

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

Correct answer

C. 1

Step-by-step solution

( aligned & C= a^2+b^2-c^2 2 a b & 60^ = a^2+b^2-c^2 2 a b & a^2+b^2-c^2=a b & a^2+b^2=a b+c^2 & Now, c(a+b)+ (a^2+b^2 ) (b+c)(c+a) = c a+b c+a b+c^2 b c+a b+c^2+a c =1 aligned )

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