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Maths-

General

Easy

Question

The minimum and maximum values of $cos space x plus 3 square root of 2 sin space open parentheses x plus pi over 4 close parentheses plus 6$ are

1,11
11,-1
6,5
5,6

hint Hint:

In this question, we have to find the minimum and maximum values of $cos space x plus 3 square root of 2 sin space open parentheses x plus pi over 4 close parentheses plus 6$ . For this first we will simplify the trigonometric function and later we can find its range as we know $a space sin space x plus b space cos space x element of open square brackets negative square root of a squared plus b squared end root comma square root of a squared plus b squared end root close square brackets$ .

The correct answer is: 1,11

$cos space x plus 3 square root of 2 sin space open parentheses x plus pi over 4 close parentheses plus 6 equals cos space x space plus 3 square root of 2 open parentheses sin space x. cos straight pi over 4 plus cos space x. sin straight pi over 4 close parentheses equals cos space x plus 3 square root of 2 sin space x. fraction numerator 1 over denominator square root of 2 end fraction plus 3 square root of 2. fraction numerator 1 over denominator square root of 2 end fraction. cos space x equals cos space x plus 3 space sin space x plus 3 space cos space x plus 6 equals 4 cos space x plus 3 space sin space x plus 6 A s comma space minus square root of a squared plus b squared end root less or equal than a sin space x plus b cos space x less or equal than square root of a squared plus b squared end root rightwards double arrow negative 5 less or equal than 3 sin space x plus 4 space cos space x less or equal than 5 rightwards double arrow negative 5 plus 6 less or equal than 3 sin space x plus 4 space cos space x plus 6 less or equal than 5 plus 6 rightwards double arrow 1 less or equal than 3 sin space x plus 4 space cos space x less or equal than 11 S o comma space m i n i m u m space a n d space m a x i m u m space v a l u e space a r e space 1 space a n d space 11 space r e s p e c t i v e y. space$

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