If sin A +sin B +sinC =3 then what is cos A + cosB+cosC equal to ?

Options

A. `-1`
B. 0
C. 1
D. 3

Explanation

To solve the problem where \( \sin A + \sin B + \sin C = 3 \), we need to determine the value of \( \cos A + \cos B + \cos C \).

### Step-by-step Solution:

1. **Understanding the Sine Function**:
The sine function, \( \sin x \), has a maximum value of 1 for any angle \( x \). Therefore, for the equation \( \sin A + \sin B + \sin C = 3 \) to hold true, each sine term must equal its maximum value:
\[ \sin A = 1, \quad \sin B = 1, \quad \sin C = 1 \]

2. **Finding the Angles**:
The sine of an angle is equal to 1 at specific angles. The angles that satisfy \( \sin x = 1 \) are:
\[ A = 90^\circ + 360^\circ n, \quad B = 90^\circ + 360^\circ m, \quad C = 90^\circ + 360^\circ p \]
where \( n, m, p \) are any integers.

3. **Calculating the Cosine Values**:
Now, we need to find \( \cos A \), \( \cos B \), and \( \cos C \). For \( A = 90^\circ \):
\[ \cos A = \cos(90^\circ) = 0 \]
Similarly, since \( B \) and \( C \) are also \( 90^\circ \) (or equivalent angles), we have:
\[ \cos B = \cos(90^\circ) = 0 \]
\[ \cos C = \cos(90^\circ) = 0 \]

4. **Summing the Cosine Values**:
Now we can sum these values:
\[ \cos A + \cos B + \cos C = 0 + 0 + 0 = 0 \]

### Final Result:
Thus, the value of \( \cos A + \cos B + \cos C \) is:
\[ \boxed{0} \]