Browse Questions

# The maximum value of $4\sin^2x+3\cos^2x+\sin\large\frac{x}{2}$$+\cos\large\frac{x}{2} is \begin{array}{1 1}(a)\;4+\sqrt 2&(b)\;3+\sqrt 2\\(c)\;9&(d)\;4\end{array} Can you answer this question? ## 1 Answer 0 votes Maximum value of 4\sin^2x+3\cos^2x\sin^2x+3 is 4 \sin\large\frac{x}{2}$$+\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.