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BITSAT2021MathematicsTrigonometric Ratios & IdentitiesActual

If A + B + C = 2 then

Options

  1. AA B+ B C+ C A=1
  2. BA+ B+ C= A B C
  3. C2 ~A + 2 ~B + 2 C =1+4 A B C
  4. DAll three are correct

Correct answer

D. All three are correct

Step-by-step solution

B + C = 2 - A ( B + C )= A B + C 1- B C = A A B + B C + C A =1 A B C ( C + A + B )=1 A + B + C = A B C Again 2 ~A + 2 ~B + 2 C =2 ( A + B ) ( A - B )+ 2 C =2 ( 2 -C ) (A-B)+1-2 ² C=2 C[ (A-B)- C]+1=2 C [ ( A - B )- 2 -( A + B ) ]+1 array l =2 C[ (A-B)- (A+B)]+1 =4 A B C+1 array

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