Find the value of `(cos(45^@-A))/(sin(45^@+A))`

Answer

To find the value of the expression \(\frac{\cos(45^\circ - A)}{\sin(45^\circ + A)}\), we can follow these steps:

### Step 1: Use the identity for cosine
We know that \(\cos(45^\circ - A)\) can be expressed using the sine function:
\[ \cos(45^\circ - A) = \sin(90^\circ - (45^\circ - A)) = \sin(45^\circ + A) \]

### Step 2: Substitute into the expression
Now, we substitute \(\cos(45^\circ - A)\) in the original expression:
\[ \frac{\cos(45^\circ - A)}{\sin(45^\circ + A)} = \frac{\sin(45^\circ + A)}{\sin(45^\circ + A)} \]

### Step 3: Simplify the expression
Since the numerator and denominator are the same, we can simplify:
\[ \frac{\sin(45^\circ + A)}{\sin(45^\circ + A)} = 1 \]

### Final Answer
Thus, the value of the expression \(\frac{\cos(45^\circ - A)}{\sin(45^\circ + A)}\) is:
\[ \boxed{1} \]

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