Question

$\alpha,\beta,\gamma$ are real numbers satisfying $\cot\frac{A}{2}\cot\frac{B}{2}\cot\frac{C}{2}$. The minimum value of the given expression $\sin\alpha + \sin\beta + \sin\gamma$ is

• A. Zero
• B. – 3
• C. Positive
• D. Negative

Answer 1

Answer: (C)

Positive

Answer 2

Since $\sin\alpha + \sin\beta + \sin\gamma > \sin(\alpha + \beta + \gamma)$

when $\alpha + \beta + \gamma = \pi$.

$\therefore$ $\sin\alpha + \sin\beta + \sin\gamma > 0$

$\therefore$The minimum value of $\sin\alpha + \sin\beta + \sin\gamma$ is always positive.