Find the value of `(sin43^(@))/(cos47^(@))`.

Options

A. 0
B. 1
C. `sin43^(@)`
D. `cos47^(@)`

Answer

To find the value of \(\frac{\sin 43^\circ}{\cos 47^\circ}\), we can follow these steps:

### Step 1: Recognize the relationship between the angles
We know that:
\[ 43^\circ = 90^\circ - 47^\circ \]

### Step 2: Use the co-function identity
Using the co-function identity, we can express \(\sin(90^\circ - \theta)\) as \(\cos(\theta)\):
\[ \sin(43^\circ) = \sin(90^\circ - 47^\circ) = \cos(47^\circ) \]

### Step 3: Substitute into the original expression
Now we can substitute \(\sin(43^\circ)\) in our original expression:
\[ \frac{\sin 43^\circ}{\cos 47^\circ} = \frac{\cos 47^\circ}{\cos 47^\circ} \]

### Step 4: Simplify the expression
Since \(\cos 47^\circ\) in the numerator and denominator are the same, we can simplify:
\[ \frac{\cos 47^\circ}{\cos 47^\circ} = 1 \]

### Final Answer
Thus, the value of \(\frac{\sin 43^\circ}{\cos 47^\circ}\) is:
\[ \boxed{1} \]