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Q.
The maximum value of $f ( x )=\sin x (1+\cos x )$ is
Application of Derivatives
Solution:
$\Theta f(x)=\sin x(1+\cos x)=\sin x+\frac{\sin 2 x}{2}$
$\Rightarrow f ^{\prime}( x )=\cos x +\cos 2 x =2 \cos ^2 x +\cos x -1=(\cos x +1)(2 \cos x -1)$
$\therefore f ( x )$ is maximum at $x =\frac{\pi}{3}$
$\therefore f \left(\frac{\pi}{3}\right)=\frac{\sqrt{3}}{2}\left(1+\frac{1}{2}\right)=\frac{3 \sqrt{3}}{4}$
