A) 1
B) \[\frac{3}{4}\]
C) \[\frac{1}{2}\]
D) \[\frac{1}{4}\]
Correct Answer: C
Solution :
\[\therefore sin\theta ~-cos\theta ~=0~\therefore sin\theta ~=cos\theta \] Since, \[sin\theta \]and \[cos\theta ~\] are equal for \[\theta \] = 45° So, \[si{{n}^{4}}\theta ~+co{{s}^{4}}\theta ~={{\left( sin\text{ }45{}^\circ \right)}^{4}}+{{\left( cos\text{ }45{}^\circ \right)}^{4}}\] = \[{{\left( \frac{1}{\sqrt{2}} \right)}^{4}}+{{\left( \frac{1}{\sqrt{2}} \right)}^{4}}\] = \[\frac{1}{4}+\frac{1}{4}=\frac{1+1}{4}=\frac{2}{4}=\frac{\mathbf{1}}{\mathbf{2}}\]
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