If tan theta = frac{sin alpha - cos alpha}{si | vedclass

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(D) Given $	an 	heta = \frac{\sin \alpha - \cos \alpha}{\sin \alpha + \cos \alpha}$.Dividing the numerator and denominator by $\cos \alpha$,we get $

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$\sin 2 \alpha$

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(D) Given $	an 	heta = \frac{\sin \alpha - \cos \alpha}{\sin \alpha + \cos \alpha}$.Dividing the numerator and denominator by $\cos \alpha$,we get $	an 	heta = \frac{	an \alpha - 1}{	an \alpha + 1}$.We know that $	an(\frac{\pi}{4}) = 1$,so $	an 	heta = \frac{	an \alpha - 	an(\frac{\pi}{4})}{1 + 	an \alpha 	an(\frac{\pi}{4})}$.Using the formula $	an(A - B) = \frac{	an A - 	an B}{1 + 	an A 	an B}$,we get $	an 	heta = 	an(\alpha - \frac{\pi}{4})$.Thus,$	heta = \alpha - \frac{\pi}{4}$.Then $2 	heta = 2 \alpha - \frac{\pi}{2}$.Therefore,$\cos 2 	heta = \cos(2 \alpha - \frac{\pi}{2})$.Using the identity $\cos(x - \frac{\pi}{2}) = \sin x$,we get $\cos 2 	heta = \sin 2 \alpha$.

If $\tan \theta = \frac{\sin \alpha - \cos \alpha}{\sin \alpha + \cos \alpha}$ and $0 \leq \alpha \leq \frac{\pi}{2}$,then the value of $\cos 2 \theta$ is

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