Value of `sin(37^circ)cos(53^circ)` is

Options

A. `(9)/(25)`
B. `(12)/(25)`
C. `(16)/(25)`
D. `(3)/(5)`

Explanation

To find the value of \( \sin(37^\circ) \cos(53^\circ) \), we can use some trigonometric identities and known values.

### Step-by-Step Solution:

1. **Identify the relationship between angles**:
We know that \( \cos(53^\circ) \) can be expressed in terms of \( \sin(37^\circ) \) because \( 53^\circ = 90^\circ - 37^\circ \). Therefore, we can use the co-function identity:
\[ \cos(53^\circ) = \sin(37^\circ) \]

2. **Use known values**:
From trigonometric tables or standard results, we have:
\[ \sin(37^\circ) \approx \frac{3}{5} \]
and
\[ \cos(53^\circ) = \sin(37^\circ) \approx \frac{3}{5} \]

3. **Substitute the values**:
Now substituting the known values into the expression:
\[ \sin(37^\circ) \cos(53^\circ) = \sin(37^\circ) \sin(37^\circ) = \left(\frac{3}{5}\right) \left(\frac{3}{5}\right) \]

4. **Calculate the product**:
\[ \sin(37^\circ) \cos(53^\circ) = \frac{3}{5} \cdot \frac{3}{5} = \frac{9}{25} \]

5. **Final answer**:
Therefore, the value of \( \sin(37^\circ) \cos(53^\circ) \) is:
\[ \frac{9}{25} \]