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    Question

    alpha plus beta plus gamma equals 2 pi comma then

    1. tan invisible function application fraction numerator alpha over denominator 2 end fraction plus tan invisible function application fraction numerator beta over denominator 2 end fraction+tan invisible function application fraction numerator gamma over denominator 2 end fraction equals tan invisible function application fraction numerator alpha over denominator 2 end fraction tan invisible function application fraction numerator beta over denominator 2 end fraction tan invisible function application fraction numerator gamma over denominator 2 end fraction  
    2. tan invisible function application fraction numerator alpha over denominator 2 end fraction tan invisible function application fraction numerator beta over denominator 2 end fraction plus tan invisible function application fraction numerator beta over denominator 2 end fraction tan invisible function application fraction numerator gamma over denominator 2 end fraction+tan invisible function application fraction numerator gamma over denominator 2 end fraction tan invisible function application fraction numerator alpha over denominator 2 end fraction equals 1  
    3. tan invisible function application fraction numerator alpha over denominator 2 end fraction plus tan invisible function application fraction numerator beta over denominator 2 end fraction+tan invisible function application fraction numerator gamma over denominator 2 end fraction equals negative tan invisible function application fraction numerator alpha over denominator 2 end fraction tan invisible function application fraction numerator beta over denominator 2 end fraction tan invisible function application fraction numerator gamma over denominator 2 end fraction  
    4. None of these  

    The correct answer is: tan invisible function application fraction numerator alpha over denominator 2 end fraction plus tan invisible function application fraction numerator beta over denominator 2 end fraction+tan invisible function application fraction numerator gamma over denominator 2 end fraction equals tan invisible function application fraction numerator alpha over denominator 2 end fraction tan invisible function application fraction numerator beta over denominator 2 end fraction tan invisible function application fraction numerator gamma over denominator 2 end fraction

      alpha plus beta plus gamma equals 2 pi rightwards double arrow fraction numerator alpha over denominator 2 end fraction plus fraction numerator beta over denominator 2 end fraction plus fraction numerator gamma over denominator 2 end fraction equals pi
      therefore tan invisible function application open parentheses fraction numerator alpha over denominator 2 end fraction plus fraction numerator beta over denominator 2 end fraction close parentheses equals tan invisible function application open parentheses pi minus fraction numerator gamma over denominator 2 end fraction close parentheses equals negative tan invisible function application fraction numerator gamma over denominator 2 end fraction
      rightwards double arrow fraction numerator tan invisible function application alpha divided by 2 plus tan invisible function application beta divided by 2 over denominator 1 minus tan invisible function application alpha divided by 2 tan invisible function application beta divided by 2 end fraction equals tan invisible function application gamma divided by 2
      rightwards double arrow tan invisible function application alpha divided by 2 plus tan invisible function application beta divided by 2 plus tan invisible function application gamma divided by 2 equals tan invisible function application alpha divided by 2 tan invisible function application beta divided by 2 tan invisible function application gamma divided by 2 left square bracket because cos to the power of 2 end exponent invisible function application theta less or equal than 1 right square bracket

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