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If $\cos \alpha+\cos \beta+\cos \gamma=0$, where $0 < \alpha \leq \frac{\pi}{2}, 0 < \beta \leq \frac{\pi}{2}$,
$0 < \gamma \leq \frac{\pi}{2}$, then what is the value of $\sin \alpha+\sin \beta+\sin \gamma ?$
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$0 < \gamma \leq \frac{\pi}{2}$, then what is the value of $\sin \alpha+\sin \beta+\sin \gamma ?$
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Verified Answer
The correct answer is:
3
$\cos \alpha+\cos \beta+\cos \gamma=0$
Given, $0 < \alpha \leq \frac{\pi}{2}, 0 < \beta \leq \frac{\pi}{2}, 0 < \gamma \leq \frac{\pi}{2}$.
(1) is satisfied when $\alpha=\frac{\pi}{2}, \beta=\frac{\pi}{2}$ and $\gamma=\frac{\pi}{2}$.
$\therefore \sin \alpha+\sin \beta+\sin \gamma=\sin \frac{\pi}{2}+\sin \frac{\pi}{2}+\sin \frac{\pi}{2} .$
$=1+1+1=3 .$
Given, $0 < \alpha \leq \frac{\pi}{2}, 0 < \beta \leq \frac{\pi}{2}, 0 < \gamma \leq \frac{\pi}{2}$.
(1) is satisfied when $\alpha=\frac{\pi}{2}, \beta=\frac{\pi}{2}$ and $\gamma=\frac{\pi}{2}$.
$\therefore \sin \alpha+\sin \beta+\sin \gamma=\sin \frac{\pi}{2}+\sin \frac{\pi}{2}+\sin \frac{\pi}{2} .$
$=1+1+1=3 .$
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