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Maths-

General

Easy

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

$- 4$
$- 3$
$- 2$
$- 1$

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
$rightwards double arrow a plus a to the power of 2 end exponent greater than 2$
$rightwards double arrow a to the power of 2 end exponent plus a minus 2 greater than 0$
$rightwards double arrow open parentheses a plus 2 close parentheses open parentheses a minus 1 close parentheses greater than 0$
$rightwards double arrow a less than negative 2$ or $blank a greater than 1$

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

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