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Maths-

General

Easy

Question

The minimum and maximum values of $2 square root of 2 cos space x plus sin space x$ are

-1,1
$- 2 \sqrt{2}, 2 \sqrt{2}$
1,8
-3,3

hint Hint:

In this question, we have to find the maximum and minimum value of the given function. As we know, minimum and maximum value of a sin x + b cos x is $negative square root of a squared plus b squared end root a n d space space square root of a squared plus b squared end root$ , so we can now find the required value.

The correct answer is: -3,3

f(x) = $2 square root of 2 cos space x plus sin space x$
As minimum and maximum value of a sin x + b cos x is $negative square root of a squared plus b squared end root a n d space space square root of a squared plus b squared end root$
So, minimum value $equals negative square root of 1 squared plus open parentheses 2 square root of 2 close parentheses squared end root equals negative square root of 9 equals negative 3$
Maximum value = $equals square root of 1 squared plus open parentheses 2 square root of 2 close parentheses squared end root equals square root of 9 equals 3$

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