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 can follow these steps:

### Step 1: Use the Complementary Angle Identity
Recall that \(\cos(90^\circ - \theta) = \sin(\theta)\). We can rewrite \(\cos 70^\circ\) and \(\cos 59^\circ\) using this identity.

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

### Step 2: Substitute the Values
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:

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

### Step 4: Calculate \(\sin 30^\circ\)
We know that \(\sin 30^\circ = \frac{1}{2}\). Therefore, we can calculate \(\sin^2 30^\circ\):

\[ \sin^2 30^\circ = \left(\frac{1}{2}\right)^2 = \frac{1}{4}. \]

### Step 5: Substitute Back into the Expression
Now substitute \(\sin^2 30^\circ\) back into the expression:

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

### Step 6: Simplify the Expression
This simplifies to:

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

### Final Answer
Thus, the evaluated expression is:

\[ \boxed{0}. \]