Answer
$$\cos^2\theta(\tan^2\theta+1)=1$$
We simplify the left side first. It is proved to be an identity.
Work Step by Step
$$\cos^2\theta(\tan^2\theta+1)=1$$
We simplify the left side, since it is obviously more complex.
$$A=\cos^2\theta(\tan^2\theta+1)$$
We can change $\tan^2\theta+1$ according to the following Pythagorean Identity:
$$\tan^2\theta+1=\sec^2\theta$$
Also from a Reciprocal Identity, $$\sec\theta=\frac{1}{\cos\theta}$$
That means $$\sec^2\theta=\frac{1}{\cos^2\theta}$$
Therefore, $$\tan^2\theta+1=\frac{1}{\cos^2\theta}$$
We now apply it into $A$:
$$A=\cos^2\theta\times\frac{1}{\cos^2\theta}$$
$$A=1$$
The left side and right side are equal. The trigonometric expression is an identity.