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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Trignometry
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The maximum value of $4\sin^2x+3\cos^2x+\sin\large\frac{x}{2}$$+\cos\large\frac{x}{2}$ is

\begin{array}{1 1}(a)\;4+\sqrt 2&(b)\;3+\sqrt 2\\(c)\;9&(d)\;4\end{array}

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Maximum value of $4\sin^2x+3\cos^2x\sin^2x+3$ is 4
$\sin\large\frac{x}{2}$$+\cos\large\frac{x}{2}=\large\frac{1}{\sqrt 2}+\frac{1}{\sqrt 2}$
$\qquad\qquad\quad\;\;=\sqrt 2$
both attained at $x=\large\frac{\pi}{4}$.
Hence the given function has maximum value is $4+\sqrt 2$
Hence (a) is the correct answer.
answered Oct 7, 2013 by sreemathi.v
 

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