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Maths-

General

Easy

Question

$text If end text a less or equal than 16 s i n invisible function application x c o s invisible function application x plus 12 c o s to the power of 2 end exponent invisible function application x minus 6 less or equal than b text for all end text x element of R comma$ then

$a = - 5, b = 5$
$a = - 4, b = 4$
$a = - 10, b = 10$
$None of these$

The correct answer is: $a equals negative 10 comma b equals 10$

We have
$16 sin invisible function application x times cos invisible function application x plus 12 cos to the power of 2 end exponent invisible function application x minus 6 equals 8 sin invisible function application 2 x plus 6 cos invisible function application 2 x$
Now
$square root of 8 to the power of 2 end exponent plus 6 to the power of 2 end exponent end root less or equal than 8 s i n invisible function application 2 x plus 6 c o s invisible function application 2 x less or equal than square root of 8 to the power of 2 end exponent plus 6 to the power of 2 end exponent end root$
$rightwards double arrow negative 10 less or equal than 8 s i n invisible function application 2 x plus 6 c o s invisible function application 2 x less or equal than 10$
$text Hence, end text a minus negative 10 comma b minus 10$

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