A) \[\frac{1}{4}\]
B) \[\frac{1}{2}\]
C) \[\frac{3}{4}\]
D) 1
Correct Answer: B
Solution :
Given, \[\sin \,\theta -\cos \theta =0\] \[\Rightarrow \,\,\sin \theta =\cos \theta \] \[\Rightarrow \,\tan \theta =1=\tan \,45{}^\circ \Rightarrow \theta =45{}^\circ \] \[\therefore \,\,\,{{\sin }^{4}}\theta +{{\cos }^{4}}\theta ={{\sin }^{4}}45{}^\circ +{{\cos }^{4}}45{}^\circ \] \[={{\left( \frac{1}{\sqrt{2}} \right)}^{4}}+{{\left( \frac{1}{\sqrt{2}} \right)}^{4}}=\frac{1}{4}+\frac{1}{4}=\frac{1}{2}\]
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