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I f blank x subscript 1 end subscript blank a n d blank x subscript 2 end subscript are two distinct roots of the equation a cos invisible function application x plus b sin invisible function application x equals c comma blank t h e n tan invisible function application fraction numerator x subscript 1 end subscript plus x subscript 2 end subscript over denominator 2 end fraction is equal to

  1. fraction numerator a over denominator b end fraction  
  2. fraction numerator b over denominator a end fraction  
  3. fraction numerator c over denominator a end fraction  
  4. fraction numerator a over denominator c end fraction  

The correct answer is: fraction numerator b over denominator a end fraction


    a cos invisible function application x plus b sin invisible function application x equals c
    rightwards double arrow fraction numerator a open parentheses 1 minus tan to the power of 2 end exponent invisible function application fraction numerator x over denominator 2 end fraction close parentheses over denominator 1 plus tan to the power of 2 end exponent invisible function application fraction numerator x over denominator 2 end fraction end fraction plus fraction numerator 2 b tan invisible function application fraction numerator x over denominator 2 end fraction over denominator 1 plus tan to the power of 2 end exponent invisible function application fraction numerator x over denominator 2 end fraction end fraction equals c
    rightwards double arrow open parentheses c plus a close parentheses tan to the power of 2 end exponent invisible function application fraction numerator x over denominator 2 end fraction minus 2 b tan invisible function application fraction numerator x over denominator 2 end fraction plus c minus a equals 0
    rightwards double arrow tan invisible function application fraction numerator x subscript 1 end subscript over denominator 2 end fraction plus tan invisible function application fraction numerator x subscript 2 end subscript over denominator 2 end fraction equals fraction numerator 2 b over denominator c plus a end fraction a n d tan invisible function application fraction numerator x subscript 1 end subscript over denominator 2 end fraction tan invisible function application fraction numerator x subscript 2 end subscript over denominator 2 end fraction equals fraction numerator c minus a over denominator c plus a end fraction
    rightwards double arrow tan invisible function application open parentheses fraction numerator x subscript 1 end subscript plus x subscript 2 end subscript over denominator 2 end fraction close parentheses equals fraction numerator fraction numerator 2 b over denominator c plus a end fraction over denominator 1 minus fraction numerator c minus a over denominator c plus a end fraction end fraction equals fraction numerator 2 b over denominator 2 a end fraction equals fraction numerator b over denominator a end fraction

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