Solve `cosec^(2)theta-cot^(2) theta=cos theta`.

Explanation

To solve the equation \( \csc^2 \theta - \cot^2 \theta = \cos \theta \), we can follow these steps:

### Step 1: Rewrite the left-hand side using trigonometric identities
We know from trigonometric identities that:
\[ \csc^2 \theta - \cot^2 \theta = 1 \]
Thus, we can rewrite the equation as:
\[ 1 = \cos \theta \]

### Step 2: Solve for \( \theta \)
The equation \( \cos \theta = 1 \) is satisfied when:
\[ \theta = 2n\pi \quad \text{for any integer } n \]
This is because the cosine function equals 1 at integer multiples of \( 2\pi \).

### Step 3: Write the general solution
The general solution for the equation is:
\[ \theta = 2n\pi \quad (n \in \mathbb{Z}) \]

### Summary of the solution
The solution to the equation \( \csc^2 \theta - \cot^2 \theta = \cos \theta \) is:
\[ \theta = 2n\pi \quad (n \in \mathbb{Z}) \]