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If $$\sin(\theta) - \cos(\theta) = 0$$ , the value of $$\sin^{4}(\theta) + \cos^{4}(\theta)$$ is:
Given , $$\sin(\theta)= \cos(\theta)$$ .
$$\tan(\theta)$$ = 1
this implies, $$\sin(\theta)= \cos(\theta)$$ = $$\dfrac{\ 1}{\sqrt{2}}$$
Therefore , $$\sin^{4}(\theta) + \cos^{4}(\theta)$$ = $$\dfrac{\ 1}{4}+\dfrac{\ 1}{4}$$ = $$\dfrac{\ 1}{2}$$.
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