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MHT CET20242 May 2024Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

In ABC , with usual notations, if 1 b+c + 1 c+a = 3 a+b+c , then m C is equal to

Options

  1. A3
  2. B2
  3. C4
  4. D6

Correct answer

A. 3

Step-by-step solution

aligned & 1 b+c + 1 c+a = 3 a+b+c & a+b+c b+c + a+b+c c+a = 3(a+b+c) a+b+c & a b+c +1+ b c+a +1=3 & a b+c + b c+a =1 & a(c+a)+b(b+c)=(b+c)(c+a) & a c+a^2+b^2+b c=b c+a b+c^2+a c & a^2+b^2-c^2=a b ...(i) aligned By cosine Rule, aligned & C= a^2+b^2-c^2 2 a b & C= a b 2 a b & C= 1 2 & C= 3 aligned ...[From (i)]

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