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Question

If the inequality sin to the power of 2 end exponent invisible function application x plus a cos invisible function application x plus a to the power of 2 end exponent greater than 1 plus cos invisible function application x holds for any x element of R comma then the largest negative integral value of a is

  1. negative 4  
  2. negative 3  
  3. negative 2  
  4. negative 1  

The correct answer is: negative 3


    sin to the power of 2 end exponent invisible function application x plus a cos invisible function application x plus a to the power of 2 end exponent greater than 1 plus cos invisible function application x
    Putting x equals 0 comma we get
    rightwards double arrow a plus a to the power of 2 end exponent greater than 2
    rightwards double arrow a to the power of 2 end exponent plus a minus 2 greater than 0
    rightwards double arrow open parentheses a plus 2 close parentheses open parentheses a minus 1 close parentheses greater than 0
    rightwards double arrow a less than negative 2 orblank a greater than 1

    Therefore, we have the largest negative integral value of a equals negative 3

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