Simplify ( theta)/( theta).

Using the quotient identity, we have:

$$\frac{\cos \theta}{\sin \theta} = \cot \theta$$

The correct option is 1.
The final answer is $\boxed{\text{1) } \cot \theta}$.

Using the Pythagorean identity, we have:

$$1 + \tan^2 \theta = \sec^2 \theta$$

The correct option is 1.
The final answer is $\boxed{\text{1) } \sec^2 \theta}$.

We know that $\tan(60^\circ) = \sqrt{3}$.
Since $\cot \theta = \frac{1}{\tan \theta}$:

$$\cot(60^\circ) = \frac{1}{\tan(60^\circ)} = \frac{1}{\sqrt{3}}$$

The correct option is 3.
The final answer is $\boxed{\text{3) } \frac{1}{\sqrt{3}}}$.

We know that $\sec \theta = \frac{1}{\cos \theta}$.
Since $\cos(90^\circ) = 0$:

$$\sec(90^\circ) = \frac{1}{\cos(90^\circ)} = \frac{1}{0}$$

The value is undefined.
The correct option is 3.
The final answer is $\boxed{\text{3) undefined}}$.

We know that $\tan(60^\circ) = \sqrt{3}$.
Therefore:

$$\theta = 60^\circ$$

The correct option is 3.
The final answer is $\boxed{\text{3) } 60^\circ}$.

Using the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$:

$$\left(\frac{3}{5}\right)^2 + \cos^2 \theta = 1$$ $$\frac{9}{25} + \cos^2 \theta = 1$$ $$\cos^2 \theta = 1 - \frac{9}{25}$$ $$\cos^2 \theta = \frac{25 - 9}{25}$$ $$\cos^2 \theta = \frac{16}{25}$$ $$\cos \theta = \pm \sqrt{\frac{16}{25}}$$ $$\cos \theta = \pm \frac{4}{5}$$

Since $\theta$ is acute (in the first quadrant), $\cos \theta$ must be positive.

$$\cos \theta = \frac{4}{5}$$

The correct option is 1.
The final answer is $\boxed{\text{1) } \frac{4}{5}}$.

Given the equation:

$$\sin \theta - \cos \theta = 0$$ $$\sin \theta = \cos \theta$$

Divide both sides by $\cos \theta$ (assuming $\cos \theta \neq 0$):

$$\frac{\sin \theta}{\cos \theta} = 1$$ $$\tan \theta = 1$$

We know that $\tan(45^\circ) = 1$.
Therefore:

$$\theta = 45^\circ$$

The correct option is 2.
The final answer is $\boxed{\text{2) } 45^\circ}$.

Using the Pythagorean identity $\csc^2 \theta - \cot^2 \theta = 1$.
Factor the left side as a difference of squares:

$$(\csc \theta - \cot \theta)(\csc \theta + \cot \theta) = 1$$

Substitute the given value $(\csc \theta - \cot \theta) = x$:

$$x(\csc \theta + \cot \theta) = 1$$

Solve for $(\csc \theta + \cot \theta)$:

$$\csc \theta + \cot \theta = \frac{1}{x}$$

The correct option is 1.
The final answer is $\boxed{\text{1) } \frac{1}{x}}$.

This is the double angle formula for cosine:

$$\frac{1 - \tan^2 \theta}{1 + \tan^2 \theta} = \cos(2\theta)$$

The correct option is 1.
The final answer is $\boxed{\text{1) } \cos(2\theta)}$.