Evaluate :
`(cos 70^(@))/(sin 20^(@))+(cos 59^(@))/(sin31^(@))-8sin^(2)30^(@)`

Answer

To evaluate the expression

\[ \frac{\cos 70^\circ}{\sin 20^\circ} + \frac{\cos 59^\circ}{\sin 31^\circ} - 8\sin^2 30^\circ, \]

we will follow these steps:

### Step 1: Use the co-function identity
We know that

\[ \sin(90^\circ - \theta) = \cos(\theta). \]

Using this identity, we can rewrite \(\cos 70^\circ\) and \(\cos 59^\circ\):

\[ \cos 70^\circ = \sin(90^\circ - 70^\circ) = \sin 20^\circ, \]
\[ \cos 59^\circ = \sin(90^\circ - 59^\circ) = \sin 31^\circ. \]

### Step 2: Substitute in the expression
Now, we can substitute these values back into the expression:

\[ \frac{\sin 20^\circ}{\sin 20^\circ} + \frac{\sin 31^\circ}{\sin 31^\circ} - 8\sin^2 30^\circ. \]

### Step 3: Simplify the fractions
The fractions simplify to:

\[ 1 + 1 - 8\sin^2 30^\circ. \]

### Step 4: Calculate \(\sin 30^\circ\)
We know that:

\[ \sin 30^\circ = \frac{1}{2}. \]

### Step 5: Substitute \(\sin 30^\circ\) into the expression
Now, substituting \(\sin 30^\circ\) into the expression gives:

\[ 1 + 1 - 8\left(\frac{1}{2}\right)^2. \]

### Step 6: Calculate \(\sin^2 30^\circ\)
Calculating \(\left(\frac{1}{2}\right)^2\):

\[ \left(\frac{1}{2}\right)^2 = \frac{1}{4}. \]

### Step 7: Substitute \(\sin^2 30^\circ\) into the expression
Now substituting this back gives:

\[ 1 + 1 - 8 \cdot \frac{1}{4}. \]

### Step 8: Simplify the expression
Calculating \(8 \cdot \frac{1}{4} = 2\):

\[ 1 + 1 - 2 = 2 - 2 = 0. \]

### Final Answer
Thus, the final answer is:

\[ \boxed{0}. \]