Q60 / 120 · VITEEE 2012 · Mathematics
Themaximum value of $4 \sin ^{2} x-12 \sin x+7$ is
- A25
- B4
- Cdoes not exist
- Correct answerDNone of these
Solution
$$
\begin{array}{l}
\begin{array}{l}
4 \sin ^{2} x-12 \sin x+7 \\
=4\left(\sin ^{2} x-3 \sin x\right)+7 \\
=4\left[\left(\sin x-\frac{3}{2}\right)^{2}-\frac{9}{4}\right]+7 \\
=4\left(\sin x-\frac{3}{2}\right)^{2}-9+7 \\
=4\left(\sin x-\frac{3}{2}\right)^{2}-2
\end{array} \\
\qquad \begin{array}{l}
=4 \\
=4
\end{array}
\end{array}
$$
Hence, the correct answer is option: 'D'.