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# Write the Maximum Value of 12 Sin X − 9 Sin2 X. - CBSE (Science) Class 11 - Mathematics

ConceptTrigonometric Functions of Sum and Difference of Two Angles

#### Question

Write the maximum value of 12 sin x − 9 sin2 x

#### Solution

$\text{ Let } f\left( x \right) = 12\sin x - 9 \sin^2 x$
$= - \left( 9 \sin^2 x - 12 \sin x \right)$
$= - \left[ \left( 3\sin x \right)^2 - 2 . 3 \sin x . 2 + 2^2 - 4 \right]$
$= - \left[ \left( 3 \sin x - 2 \right)^2 - 4 \right]$
$= 4 - \left( 3 \sin x - 2 \right)^2$
$\text{ Minimum value of } \left( 3 \sin x - 2 \right)^2 is 0 .$
$\text{ Therefore, maximum value of} 4 - \left( 3 \sin x - 2 \right)^2 \text{ would be } 4 .$

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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
Q: 4 | Page no. 26
Solution Write the Maximum Value of 12 Sin X − 9 Sin2 X. Concept: Trigonometric Functions of Sum and Difference of Two Angles.
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