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 follow these steps:

### Step 1: Identify the values of \( \sin(37^\circ) \) and \( \cos(53^\circ) \)
We know that:
- The sine of an angle can be related to the cosine of its complementary angle. Specifically, \( \sin(90^\circ - \theta) = \cos(\theta) \).
- Therefore, \( \cos(53^\circ) = \sin(90^\circ - 53^\circ) = \sin(37^\circ) \).

### Step 2: Use known values
From trigonometric tables or known values:
- \( \sin(37^\circ) = \frac{3}{5} \)
- Since \( \cos(53^\circ) = \sin(37^\circ) \), we also have \( \cos(53^\circ) = \frac{3}{5} \).

### Step 3: Substitute the values into the expression
Now we can substitute these values into the expression:
\[ \sin(37^\circ) \cos(53^\circ) = \left(\frac{3}{5}\right) \left(\frac{3}{5}\right) \]

### Step 4: Perform the multiplication
Now we multiply the fractions:
\[ \sin(37^\circ) \cos(53^\circ) = \frac{3 \times 3}{5 \times 5} = \frac{9}{25} \]

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