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AP EAMCET201922 Apr 2019Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If (A B C ) is not a right angled triangle and ( ( 4 -A ) ( 4 -B )=- 1 2 2 cosec ( 4 -C ) ), then ( A B+ B C+ C A= )

Options

  1. A( A+ B+ C )
  2. B( A+ B+ C )
  3. C( 1 A+ B+ C )
  4. D( 1 A+ B+ C )

Correct answer

B. ( A+ B+ C )

Step-by-step solution

Given, (A+B+C= ) We know that, ( (A+B+C)= A B C(l- A B ) (- B C- A C) ) and ( A+ B+ C= A B C ) Now, ( ( 4 -A ) ( 4 -B ) ( 4 -C )=- 1 2 2 ) ( ( 1 3 )^3( A- A)( B- B) ) (( C- C)=- 1 2 2 ) ( A B C(1- A)(1- B) ) ((1- C)=-1 ) ( A B C(1- A- B- C ) (+ A B+ B C+ A C ) (- A B C) ) (= A B C(1- A B ) (- B C- A C) ) (= (A+B+C) ) (( A+B+C= ) ) ( 1-2( A+ B+ C)+ A B ) (+ B C+ A C ) (= l - A B- B C- A C ) ( -2( A+ B+ C)=-2( A B ) (+ B C+ A C) ) ( A B+ B C+ A C ) (= A+ B+ C )

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