# The period of the function f(x)=cos^3x+sin^3x is

Solution:      $f(x)=\cos^{3}x+\sin^{3}x$

$f(x)=\frac{1}{4}[3(\sin x+\cos x)-\sin 3x+\cos 3x].$

Now ,       $pd(\sin x)=2\pi;pd(\cos x)=2\pi,$

$pd(\sin x+\cos x)=2\pi,pd(\sin 3x)=\frac{2\pi}{3}$ and $pd(\cos 3x)=\frac{2\pi}{3}.$

$\therefore$                 $pd(f)=LCM\{\frac{2\pi}{1},\frac{2\pi}{3}\}=\frac{LCM\{2\pi,2\pi\}}{HCF\{1,3\}}=2\pi.$

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