A) 1
B) 2
C) 3
D) \[\frac{1}{4}\]
Correct Answer: D
Solution :
\[\sin \theta \,\,\cos \theta \,\,=\frac{1}{2}\] \[2\text{ }sin\theta \text{ }cos\theta =1\] \[\Rightarrow \,\,\,\theta =45{}^\circ \] \[{{\sin }^{6}}\theta +{{\cos }^{6}}\theta ={{(\sin 45{}^\circ )}^{6}}+{{(\cos \,45{}^\circ )}^{6}}\] \[=\,\,\,{{\left( \frac{1}{\sqrt{2}} \right)}^{6}}+{{\left( \frac{1}{\sqrt{2}} \right)}^{6}}=\frac{1}{8}+\frac{1}{8}=\underline{\frac{\mathbf{1}}{\mathbf{4}}}\]
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