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AP EAMCET202423 May 2024Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If A. B. C are the angles of a triangle, then A+ B+ C ^2 A 2 - ^2 B 2 + ^2 C 2 -1 =

Options

  1. A-2 B 2
  2. B-2 B 2
  3. C2 B 2
  4. D2 B 2

Correct answer

B. -2 B 2

Step-by-step solution

aligned & A+ B+ C ^2 A 2 - ^2 B 2 + ^2 C 2 -1 = & 2 A+B 2 A-B 2 +2 C 2 C 2 ( A+B 2 ) ( A-B 2 )- ^2 C 2 = & 2 ( 2 - C 2 ) ( A-B 2 )+2 C 2 C 2 ( 2 - C 2 ) ( A-B 2 )- ^2 C 2 = & 2 C 2 [ ( A-B 2 )+ C 2 ] C 2 [ ( A-B 2 )- C 2 ] = & 2 C 2 [ ( A-B 2 )+ A+B 2 ] C 2 [ ( A-B 2 )- ( A+B 2 ) ] = & 2 C 2 2 A 2 B 2 - C 2 2 A 2 B 2 =-2 B 2 . aligned

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