Find the value of the expression
`sec610^@cosec160^@-cot380^@tan470^@`

Explanation

To solve the expression \( \sec 610^\circ \cdot \csc 160^\circ - \cot 380^\circ \cdot \tan 470^\circ \), we will simplify each term step by step.

### Step 1: Simplify \( \sec 610^\circ \)

We know that the secant function has a periodicity of \( 360^\circ \). Thus, we can reduce \( 610^\circ \):

\[ 610^\circ - 360^\circ = 250^\circ \]

So,

\[ \sec 610^\circ = \sec 250^\circ \]

### Step 2: Simplify \( \csc 160^\circ \)

The cosecant function does not need any reduction since \( 160^\circ \) is already within the standard range. Thus,

\[ \csc 160^\circ = \csc 160^\circ \]

### Step 3: Simplify \( \cot 380^\circ \)

Again, using the periodicity of \( 360^\circ \):

\[ 380^\circ - 360^\circ = 20^\circ \]

So,

\[ \cot 380^\circ = \cot 20^\circ \]

### Step 4: Simplify \( \tan 470^\circ \)

Using the periodicity of \( 360^\circ \):

\[ 470^\circ - 360^\circ = 110^\circ \]

So,

\[ \tan 470^\circ = \tan 110^\circ \]

### Step 5: Substitute the simplified values into the expression

Now, substituting the simplified values back into the expression gives:

\[ \sec 250^\circ \cdot \csc 160^\circ - \cot 20^\circ \cdot \tan 110^\circ \]

### Step 6: Further simplify \( \sec 250^\circ \)

We know that:

\[ \sec(250^\circ) = \sec(270^\circ - 20^\circ) = -\csc(20^\circ) \]

### Step 7: Simplify \( \tan 110^\circ \)

Using the identity for tangent:

\[ \tan(110^\circ) = -\tan(70^\circ) \]

### Step 8: Substitute these values back

Now, we can substitute these values:

\[ -\csc(20^\circ) \cdot \csc(160^\circ) - \cot(20^\circ) \cdot (-\tan(70^\circ)) \]

### Step 9: Use identities

We know:

\[ \csc(160^\circ) = \csc(180^\circ - 20^\circ) = \csc(20^\circ) \]

Thus, we have:

\[ -\csc(20^\circ) \cdot \csc(20^\circ) + \cot(20^\circ) \cdot \tan(70^\circ) \]

### Step 10: Use the identity \( \tan(70^\circ) = \cot(20^\circ) \)

Now substituting this gives:

\[ -\csc^2(20^\circ) + \cot(20^\circ) \cdot \cot(20^\circ) = -\csc^2(20^\circ) + \cot^2(20^\circ) \]

### Step 11: Use the identity \( \csc^2(\theta) - \cot^2(\theta) = 1 \)

Thus, we have:

\[ -\left( \csc^2(20^\circ) - \cot^2(20^\circ) \right) = -1 \]

### Final Answer

So, the final value of the expression is:

\[ \boxed{-1} \]