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