#### Answer

$$\sqrt {\frac{1}{\cos^{2}\theta}-1}$$

#### Work Step by Step

Start with the Pythagorean Identity
$$\sin^{2}\theta+\cos^{2}\theta = 1.$$
Rearrange terms and solve for $\sin\theta$:
$$\sin^{2}\theta=1-\cos^{2}\theta$$
$$\sin\theta=\sqrt {1-\cos^{2}\theta}.$$
Next use the Tangent Identity and substitute in the above expression for $\sin\theta$:
$$\tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{\sqrt {1-\cos^{2}\theta}}{\cos\theta}=\sqrt {\frac{1}{\cos^{2}\theta}-1}.$$