Evaluate the equation:-
`(sec 70^(@))/("cosec" 20^(@)) + (sin 59^(@))/(cos 31^(@))` .

Answer

To evaluate the expression

\[ \frac{\sec 70^\circ}{\csc 20^\circ} + \frac{\sin 59^\circ}{\cos 31^\circ} \]

we will use some trigonometric identities. Let's break it down step by step.

### Step 1: Rewrite the Trigonometric Functions
We know that:
- \(\csc \theta = \frac{1}{\sin \theta}\)
- \(\sec \theta = \frac{1}{\cos \theta}\)

Thus, we can rewrite the expression as:

\[ \frac{1/\cos 70^\circ}{1/\sin 20^\circ} + \frac{\sin 59^\circ}{\cos 31^\circ} \]

### Step 2: Simplify the First Fraction
The first fraction simplifies to:

\[ \frac{\sin 20^\circ}{\cos 70^\circ} \]

Using the identity \(\cos 70^\circ = \sin(90^\circ - 70^\circ) = \sin 20^\circ\), we can rewrite it as:

\[ \frac{\sin 20^\circ}{\sin 20^\circ} = 1 \]

### Step 3: Simplify the Second Fraction
Now, let's simplify the second fraction:

\[ \frac{\sin 59^\circ}{\cos 31^\circ} \]

Using the identity \(\cos 31^\circ = \sin(90^\circ - 31^\circ) = \sin 59^\circ\), we can rewrite it as:

\[ \frac{\sin 59^\circ}{\sin 59^\circ} = 1 \]

### Step 4: Combine the Results
Now, we can combine the results from both fractions:

\[ 1 + 1 = 2 \]

### Final Answer
Thus, the value of the given expression is:

\[ \boxed{2} \]