If sec theta(cos theta+sin theta)=sqrt{2}, th | vedclass

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(D) Given: $\sec 	heta(\cos 	heta+\sin 	heta)=\sqrt{2}$Since $\sec 	heta = \frac{1}{\cos 	heta}$,we have:$\frac{1}{\cos 	heta}(\cos 	heta+\sin

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$\sqrt{2}$

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(D) Given: $\sec 	heta(\cos 	heta+\sin 	heta)=\sqrt{2}$Since $\sec 	heta = \frac{1}{\cos 	heta}$,we have:$\frac{1}{\cos 	heta}(\cos 	heta+\sin 	heta)=\sqrt{2}$$1+	an 	heta=\sqrt{2}$$	an 	heta=\sqrt{2}-1$ .....$(1)$Now,we need to find the value of $\frac{2 \sin 	heta}{\cos 	heta-\sin 	heta}$.Dividing the numerator and the denominator by $\cos 	heta$:$\frac{2 	an 	heta}{1-	an 	heta}$Substituting the value of $	an 	heta$ from equation $(1)$:$= \frac{2(\sqrt{2}-1)}{1-(\sqrt{2}-1)}$$= \frac{2(\sqrt{2}-1)}{2-\sqrt{2}}$$= \frac{2(\sqrt{2}-1)}{\sqrt{2}(\sqrt{2}-1)}$$= \frac{2}{\sqrt{2}} = \sqrt{2}$

If $\sec \theta(\cos \theta+\sin \theta)=\sqrt{2},$ then what is the value of $\frac{2 \sin \theta}{\cos \theta-\sin \theta} ?$

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