#### Answer

$$\sec^{2}\theta$$

#### Work Step by Step

Simplify
$$\sin^{2}\theta +\cos^{2}\theta +\tan^{2}\theta.$$
Use the Pythagorean Identity
$$\sin^{2}\theta+\cos^{2}\theta=1$$
to obtain
$$\sin^{2}\theta +\cos^{2}\theta +\tan^{2}\theta=1+\tan^{2}\theta.$$
Finally, use the Pythagorean Identity
$$1+\tan^{2}\theta=\sec^{2}\theta$$
to obtain
$$\sin^{2}\theta +\cos^{2}\theta +\tan^{2}\theta=\sec^{2}\theta.$$