Answer
$$\sec\theta$$
Work Step by Step
Simplify
$$\cos\theta+\sin\theta\tan\theta$$
by substituting the Tangent Identity:
$$\tan\theta=\frac{\sin\theta}{\cos\theta}$$
to obtain
$$\cos\theta+\sin\theta\tan\theta=\cos\theta+\sin\theta\bigg(\frac{\sin\theta}{\cos\theta}\bigg)=\cos\theta+\frac{\sin^{2}\theta}{\cos\theta}$$
Now multiply both the numerator and the denominator of the first term by $\cos\theta$
$$=\cos\theta\bigg(\frac{\cos\theta}{\cos\theta}\bigg)+\frac{\sin^{2}\theta}{\cos\theta}$$
$$=\frac{\cos^{2}\theta+\sin^{2}\theta}{\cos\theta}$$
Next, use the Pythagorean Identity:
$$\sin^{2}\theta+\cos^{2}\theta=1$$
and finally the Reciprocal Identity:
$$\sec\theta=\frac{1}{\cos\theta}$$
to obtain
$$\cos\theta+\sin\theta\tan\theta=\frac{1}{\cos\theta}=\sec\theta$$
