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AP EAMCET20226 Jul 2022Evening ShiftMathematicsProperties of TrianglesActual

In a A B C , if A=60^ , then b c+a + c a+b =

Options

  1. Aa+b+c
  2. B0
  3. C1
  4. Da b c

Correct answer

C. 1

Step-by-step solution

Apply cosine rule, A= b^2+c^2-a^2 2 b c Here, A=60^ aligned & 60^ = b^2+c^2-a^2 2 b c 1 2 = b^2+c^2-a^2 2 b c & b c=b^2+c^2-a^2 & b^2+c^2=b c+a^2...(i) aligned Now, aligned & b c+a + c a+b = b(a+b)+c(c+a) (c+a)(a+b) & = a b+b^2+c^2+a c a c+a^2+b c+a b & = a b+b c+a^2+a c a c+a^2+b c+a b [ from Eq. (i) ] & =1 aligned

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