<s>[INST] Operation of Sine and Cosine Use condition $\displaystyle\sin\theta-\cos\theta=\sqrt{2}$,
Please find the value of $\displaystyle\frac1{\sin^{10}\theta}+\frac1{\cos^{10}\theta}$.
 [/INST] Notice that $\sin \theta - \cos \theta = \sqrt{2} \implies \sin^{2} \theta - \sin (2\theta) + \cos^2\theta = 2 \implies \sin (2 \theta) = -1. $
But this holds iff $2\theta = \frac{4n - 1}{2}\pi \iff \theta = \frac{(4n-1) \pi}{4} $
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