If cos theta - sin theta = sqrt{2} sin theta, | vedclass

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(A) Given that $\cos 	heta - \sin 	heta = \sqrt{2} \sin 	heta$. Rearranging the terms,we get $\cos 	heta = (\sqrt{2} + 1) \sin 	heta$. To isolate

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$\sqrt{2} \cos 	heta$

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(A) Given that $\cos 	heta - \sin 	heta = \sqrt{2} \sin 	heta$. Rearranging the terms,we get $\cos 	heta = (\sqrt{2} + 1) \sin 	heta$. To isolate $\sin 	heta$,multiply both sides by $(\sqrt{2} - 1)$: $(\sqrt{2} - 1) \cos 	heta = (\sqrt{2} - 1)(\sqrt{2} + 1) \sin 	heta$. Since $(\sqrt{2} - 1)(\sqrt{2} + 1) = 2 - 1 = 1$,we have: $(\sqrt{2} - 1) \cos 	heta = \sin 	heta$. Expanding this,$\sqrt{2} \cos 	heta - \cos 	heta = \sin 	heta$. Therefore,$\cos 	heta + \sin 	heta = \sqrt{2} \cos 	heta$.

If $\cos \theta - \sin \theta = \sqrt{2} \sin \theta,$ then $\cos \theta + \sin \theta$ is equal to

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