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AP EAMCET202316 May 2023Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

In ABC ,( A + B )( B + C )( C + A )=

Options

  1. AA B C
  2. BA B C
  3. Ccosec A cosec B cosec C
  4. DA B C

Correct answer

C. cosec A cosec B cosec C

Step-by-step solution

Since ( A + B )( B + C )( C + A ) aligned & = ( A A + B B ) ( B B + C C ) ( C C + A A ) & = ( A B+ B A A B ) ( B C+ C B B C ) & ( C A+ A C C A ) aligned aligned & = (A+B) A B (B+C) B C (A+C) A C & = ( -C) A B ( -A) B C ( -B) A C & = C A B A B C B A C & = cosec A cosec B cosec C aligned

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