If the angles of `DeltaABC` are in ratio `1:1:2`, respectively (the largest angle being angle C), then the value of `(secA)/(cosecB)-(tanA)/(cotB)` is:

Options

A. `0`
B. `(1)/(2)`
C. `1`
D. `(sqrt(3))/(2)`

Answer

To solve the problem, we need to find the value of \((\sec A)/(\csc B) - (\tan A)/(\cot B)\) given that the angles of triangle \(ABC\) are in the ratio \(1:1:2\) with the largest angle being angle \(C\).

### Step-by-Step Solution:

1. **Define the Angles**:
Let the angles of triangle \(ABC\) be:
- Angle \(A = x\)
- Angle \(B = x\)
- Angle \(C = 2x\)

2. **Use the Angle Sum Property**:
According to the angle sum property of triangles, the sum of the angles in a triangle is \(180^\circ\):
\[ A + B + C = 180^\circ \]
Substituting the values we defined:
\[ x + x + 2x = 180^\circ \]
This simplifies to:
\[ 4x = 180^\circ \]

3. **Solve for \(x\)**:
Divide both sides by \(4\):
\[ x = \frac{180^\circ}{4} = 45^\circ \]

4. **Determine the Angles**:
Now we can find the measures of the angles:
- Angle \(A = 45^\circ\)
- Angle \(B = 45^\circ\)
- Angle \(C = 90^\circ\)

5. **Calculate Trigonometric Values**:
Now we need to calculate the trigonometric values:
- \(\sec A = \sec 45^\circ = \frac{1}{\cos 45^\circ} = \frac{1}{\frac{1}{\sqrt{2}}} = \sqrt{2}\)
- \(\csc B = \csc 45^\circ = \frac{1}{\sin 45^\circ} = \frac{1}{\frac{1}{\sqrt{2}}} = \sqrt{2}\)
- \(\tan A = \tan 45^\circ = 1\)
- \(\cot B = \cot 45^\circ = 1\)

6. **Substitute Values into the Expression**:
Now substitute these values into the expression:
\[ \frac{\sec A}{\csc B} - \frac{\tan A}{\cot B} = \frac{\sqrt{2}}{\sqrt{2}} - \frac{1}{1} \]

7. **Simplify the Expression**:
This simplifies to:
\[ 1 - 1 = 0 \]

### Final Answer:
Thus, the value of \((\sec A)/(\csc B) - (\tan A)/(\cot B)\) is \(0\).