Question

If $\sin A+\sin B+\sin C=3$, then $\cos A+\cos B+\cos c$ is equal to

• A. $3$
• B. $2$
• C. $1$
• D. $0$

Answer 1

The correct option is D

$0$

Explanation for the correct option.

Given that, $\sin A+\sin B+\sin C=3...\left(1\right)$.

Recall: $\sin {90}^o=1$

If we assume, $A=B=C={90}^o$ then the equation (1) is satisfied.

So, substitute $A=B=C={90}^o$in $\cos A+\cos B+\cos c$ we get:

$\begin{array}{rcl}\cos A+\cos B+\cos C& =& \cos {90}^o+\cos {90}^o+\cos {90}^o\\ & =& 0+0+0\\ & =& 0\end{array}$

Hence, option D is correct.