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Themaximum value of $4 \sin ^{2} x-12 \sin x+7$ is
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Verified Answer
The correct answer is:
None of these
$$
\begin{array}{l}
\begin{array}{l}
4 \sin ^{2} x-12 \sin x+7 \\
=4\left(\sin ^{2} x-3 \sin x\right)+7 \\
=4\left[\left(\sin x-\frac{3}{2}\right)^{2}-\frac{9}{4}\right]+7 \\
=4\left(\sin x-\frac{3}{2}\right)^{2}-9+7 \\
=4\left(\sin x-\frac{3}{2}\right)^{2}-2
\end{array} \\
\qquad \begin{array}{l}
=4 \\
=4
\end{array}
\end{array}
$$
\begin{array}{l}
\begin{array}{l}
4 \sin ^{2} x-12 \sin x+7 \\
=4\left(\sin ^{2} x-3 \sin x\right)+7 \\
=4\left[\left(\sin x-\frac{3}{2}\right)^{2}-\frac{9}{4}\right]+7 \\
=4\left(\sin x-\frac{3}{2}\right)^{2}-9+7 \\
=4\left(\sin x-\frac{3}{2}\right)^{2}-2
\end{array} \\
\qquad \begin{array}{l}
=4 \\
=4
\end{array}
\end{array}
$$
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