Evaluate `(sin35^(@))/(cos55^(@))+(sec20^(@))/("cosec"70^(@))`.

Answer

To evaluate the expression \((\sin 35^\circ)/(\cos 55^\circ) + (\sec 20^\circ)/(\csc 70^\circ)\), we can follow these steps:

### Step 1: Rewrite the trigonometric functions
We know that:
- \(\cos(90^\circ - \theta) = \sin(\theta)\)
- \(\sec(\theta) = \frac{1}{\cos(\theta)}\)
- \(\csc(\theta) = \frac{1}{\sin(\theta)}\)

Using these identities, we can rewrite the expression.

### Step 2: Simplify \(\sin 35^\circ\) and \(\cos 55^\circ\)
Notice that:
\[ \cos 55^\circ = \sin(90^\circ - 55^\circ) = \sin 35^\circ \]
Thus, we can rewrite the first part of the expression:
\[ \frac{\sin 35^\circ}{\cos 55^\circ} = \frac{\sin 35^\circ}{\sin 35^\circ} = 1 \]

### Step 3: Simplify \(\sec 20^\circ\) and \(\csc 70^\circ\)
Now, let's simplify the second part:
\[ \sec 20^\circ = \frac{1}{\cos 20^\circ} \]
And since:
\[ \csc 70^\circ = \frac{1}{\sin 70^\circ} = \frac{1}{\cos(90^\circ - 70^\circ)} = \frac{1}{\cos 20^\circ} \]
Thus, we can rewrite the second part of the expression:
\[ \frac{\sec 20^\circ}{\csc 70^\circ} = \frac{\frac{1}{\cos 20^\circ}}{\frac{1}{\cos 20^\circ}} = 1 \]

### Step 4: Combine the results
Now we can combine the results from Step 2 and Step 3:
\[ 1 + 1 = 2 \]

### Final Answer
Thus, the value of the expression \((\sin 35^\circ)/(\cos 55^\circ) + (\sec 20^\circ)/(\csc 70^\circ)\) is \(2\).

---