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

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Question

(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

Vedclass · Accepted Answer

$\sqrt{2} \cos 	heta$

Vedclass · Answer

(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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