A) \[\pi /2\]
B) \[\pi \]
C) \[2\pi \]
D) \[3\pi /2\]
Correct Answer: A
Solution :
Let \[f(x)={{\sin }^{4}}x+{{\cos }^{4}}x\] = \[{{({{\sin }^{2}}x+{{\cos }^{2}}x)}^{2}}-2{{\sin }^{2}}x{{\cos }^{2}}x\] = \[1-\frac{4{{\sin }^{2}}x{{\cos }^{2}}x}{2}=1-\frac{{{\sin }^{2}}2x}{2}\] =\[1-\frac{1}{4}(2{{\sin }^{2}}2x)=1-\left( \frac{1-\cos x}{4} \right)\] \[=\frac{3}{4}+\frac{1}{4}\cos 4x\] Hence the period of function = \[\frac{2\pi }{4}=\frac{\pi }{2}\]
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