`(cos 70^(@))/(sin 20^(@)) + (cos 59^(@))/(sin 31^(@) ) - 8 sin^(2) 30^(@)` is equal to

Options

A. 1
B. `-1`
C. 0
D. 2

Explanation

To solve the expression \((\cos 70^\circ/\sin 20^\circ) + (\cos 59^\circ/\sin 31^\circ) - 8 \sin^2 30^\circ\), we can use the properties of trigonometric functions.

### Step-by-step Solution:

1. **Identify Relationships**:
We know that \(\cos(90^\circ - \theta) = \sin(\theta)\) and \(\sin(90^\circ - \theta) = \cos(\theta)\).

2. **Rewrite the Cosine Terms**:
- For \(\cos 70^\circ\):
\[ \cos 70^\circ = \sin(90^\circ - 70^\circ) = \sin 20^\circ \]
- For \(\cos 59^\circ\):
\[ \cos 59^\circ = \sin(90^\circ - 59^\circ) = \sin 31^\circ \]

3. **Substitute in the Expression**:
Now we can rewrite the expression:
\[ \frac{\cos 70^\circ}{\sin 20^\circ} + \frac{\cos 59^\circ}{\sin 31^\circ} = \frac{\sin 20^\circ}{\sin 20^\circ} + \frac{\sin 31^\circ}{\sin 31^\circ} \]

4. **Simplify**:
Each term simplifies to 1:
\[ 1 + 1 = 2 \]

5. **Evaluate the Sine Squared Term**:
Now we need to evaluate \(8 \sin^2 30^\circ\):
\[ \sin 30^\circ = \frac{1}{2} \implies \sin^2 30^\circ = \left(\frac{1}{2}\right)^2 = \frac{1}{4} \]
Therefore,
\[ 8 \sin^2 30^\circ = 8 \times \frac{1}{4} = 2 \]

6. **Final Calculation**:
Substitute back into the expression:
\[ 2 - 2 = 0 \]

### Final Answer:
\[ 0 \]