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\sin(\theta)}{\cos^{2}(\theta)-\sin^{2}(\theta)}&=\frac{\tan(\theta)}{1-\tan(\theta)} \\ \frac{\frac{1}{2}\sin(2\theta)}{\cos^{2}(\theta)-\sin^{2}(\theta)}&= \mbox{ Use the first identity listed}\\ \frac{\frac{1}{2}\sin(2\theta)}{\cos(2\theta)}&=\mbox{ Use the second identity listed}\\ \frac{1}{2}\tan(2\theta)&= \mbox{ Replace sine over cosine with tangent}\\ \frac{1}{2}\frac{2\tan(\theta)}{1-\tan(\theta)}&= \mbox{ Use the third identity listed}\\ \frac{\tan(\theta)}{1-\tan(\theta)}&= \mbox{ Simplify}\\ \end{align*})
