Question

The minimum value of expression $\sin \alpha +\sin \beta +\sin \gamma$, where $\alpha ,\beta ,\gamma$ are positive real numbers satisfying $\alpha +\beta +\gamma =\pi$

• A. $0$
• B. $-3$
• C. $3$
• D. $-2$

Answer 1

The correct option is D $-2$

Taking $\alpha =\frac{-\pi }{2}$

$\Rightarrow \beta =\frac{-\pi }{2}$

$\Rightarrow$ and $\gamma =2\pi$

$\therefore \sin \alpha +\sin \beta +\sin \gamma =-\sin \frac{\pi }{2}-\sin \frac{\pi }{2}+\sin 2\pi$

$=-1-1-0$

$=-2$

Hence, the answer is $-2.$