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

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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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