Maths-
General
Easy

Question

I f cos invisible function application x plus cos invisible function application y minus cos invisible function application open parentheses x plus y close parentheses equals fraction numerator 3 over denominator 2 end fraction comma blank t h e n

  1. x plus y equals 0  
  2. x equals 2 y  
  3. x equals y  
  4. 2 x equals y  

The correct answer is: x equals y


    cos invisible function application x plus cos invisible function application y minus cos invisible function application open parentheses x plus y close parentheses equals fraction numerator 3 over denominator 2 end fraction
    rightwards double arrow 2 cos invisible function application open parentheses fraction numerator x plus y over denominator 2 end fraction close parentheses cos invisible function application open parentheses fraction numerator x minus y over denominator 2 end fraction close parentheses minus 2 cos to the power of 2 end exponent invisible function application open parentheses fraction numerator x plus y over denominator 2 end fraction close parentheses plus 1 equals fraction numerator 3 over denominator 2 end fraction
    rightwards double arrow 2 cos invisible function application blank to the power of 2 end exponent open parentheses fraction numerator x plus y over denominator 2 end fraction close parentheses minus 2 cos invisible function application open parentheses fraction numerator x plus y over denominator 2 end fraction close parentheses cos invisible function application open parentheses fraction numerator x minus y over denominator 2 end fraction close parentheses plus fraction numerator 1 over denominator 2 end fraction equals 0
    Now cos invisible function application open parentheses fraction numerator x plus y over denominator 2 end fraction close parentheses is always real, then discriminant greater or equal than 0
    rightwards double arrow 4 cos to the power of 2 end exponent invisible function application open parentheses fraction numerator x minus y over denominator 2 end fraction close parentheses minus 4 greater or equal than 0
    rightwards double arrow cos to the power of 2 end exponent invisible function application open parentheses fraction numerator x minus y over denominator 2 end fraction close parentheses greater or equal than 1
    rightwards double arrow cos to the power of 2 end exponent invisible function application open parentheses fraction numerator x minus y over denominator 2 end fraction close parentheses equals 1
    rightwards double arrow fraction numerator x minus y over denominator 2 end fraction equals 0 rightwards double arrow x equals y

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