A) \[n\pi \]
B) \[n\pi \pm {{\sin }^{-1}}\frac{2}{5}\]
C) \[n\pi +\frac{\pi }{6}\]
D) None of these
Correct Answer: A
Solution :
The given equation can be put in the form \[4{{\sin }^{4}}x=1-{{\cos }^{4}}x=(1-{{\cos }^{2}}x)\,(1+{{\cos }^{2}}x)\] \[\Rightarrow \] \[{{\sin }^{2}}x[4{{\sin }^{2}}x-1-(1-{{\sin }^{2}}x)]=0\] \[\Rightarrow \]\[{{\sin }^{2}}x[5{{\sin }^{2}}x-2]=0\]\[\Rightarrow \]\[\sin x=0\]or\[\sin x=\pm \sqrt{2/5}\]. Hence \[x=n\pi \] is the required answer.
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