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AP EAMCET202421 May 2024Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If A, B, C are the angles of triangle then 2 A- 2 B+ 2 C=

Options

  1. A4 A B C
  2. B4 A B C
  3. C4 A B C-1
  4. D4 A B C

Correct answer

B. 4 A B C

Step-by-step solution

Given that A, B, C are the angle of triangle A+B+C= 2 A+2 B+2 C=2 ...(i) Now, aligned & 2 A- 2 B+ 2 C=2 2 A+2 C 2 ( 2 A-2 C 2 ) & - [2 -2(A+C)] & =2 (A+C) (A-C)+ 2(A+C) & =2 (A+C) (A-C)+2 (A+C) (A+C) & =2 (A+C)[ (A-C)+ (A+C)] & =2 ( -B)[2 A C]=4 A B C . aligned

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