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Find the Maximum and Minimum Values of Each of the Following Trigonometrical Expression: 12 Sin X − 5 Cos X - CBSE (Science) Class 11 - Mathematics

ConceptTrigonometric Functions of Sum and Difference of Two Angles

Question

Find the maximum and minimum values of each of the following trigonometrical expression:

12 sin x − 5 cos

Solution

$\text{ Let } f\left( x \right) = 12 \sin x - 5 \cos x$
$\text{ We know that }$
$- \sqrt{{12}^2 + ( - 5 )^2} \leq 12 \sin x - 5 \cos x \leq \sqrt{{12}^2 + ( - 5 )^2}$
$- \sqrt{144 + 25} \leq 12 \sin x - 5 \cos x \leq \sqrt{144 + 25}$
$- 13 \leq 12 \sin x - 5 \cos x \leq 13$
$\text{ Hence the maximum and minumun values of }f\left( x \right) \text{ are 13 and - 13, respectively } .$

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APPEARS IN

RD Sharma Solution for Mathematics Class 11 (2019 to Current)
Chapter 7: Values of Trigonometric function at sum or difference of angles
Ex.7.20 | Q: 1.1 | Page no. 26
Solution Find the Maximum and Minimum Values of Each of the Following Trigonometrical Expression: 12 Sin X − 5 Cos X Concept: Trigonometric Functions of Sum and Difference of Two Angles.
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