Establish the identity. $$ (\csc \theta+\cot \theta)(\csc \theta-\cot \theta)=1 $$ Multiply and write the left side expression as the difference of two squares.

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To establish the identity:

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

we can multiply the left side using the difference of squares formula and then simplify using known trigonometric identities.

### Step 1: Apply the Difference of Squares Formula
The expression $$(a + b)(a - b)$$ is equal to $$a^2 - b^2$$. Applying this to the given expression:

$$
(\csc \theta + \cot \theta)(\csc \theta - \cot \theta) = \csc^2 \theta - \cot^2 \theta
$$

### Step 2: Use Trigonometric Identities
Recall the Pythagorean identity involving cosecant and cotangent:

$$
\csc^2 \theta = 1 + \cot^2 \theta
$$

Rearranging this identity gives:

$$
\csc^2 \theta - \cot^2 \theta = 1
$$

### Step 3: Substitute Back into the Equation
Substituting the result from the trigonometric identity back into our expression:

$$
\csc^2 \theta - \cot^2 \theta = 1
$$

Thus, we have:

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

### Conclusion
The identity is confirmed by expanding the left side as the difference of two squares and simplifying using fundamental trigonometric identities.

**Final Identity:**

$$
(\csc \theta + \cot \theta)(\csc \theta - \cot \theta) = \csc^2 \theta - \cot^2 \theta = 1
$$
$$ (\csc \theta + \cot \theta)(\csc \theta - \cot \theta) = 1 $$

Establish the identity.

Multiply and write the left side expression as the difference of two squares.

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Establish the identity. Multiply and write the left side expression as the difference of two squares.