Question

$\alpha ,\beta ,\gamma$ are real numbers satisfying $\alpha +\beta +\gamma =\pi$.

The value of the given expression

$sin\alpha +sin\beta +sin\gamma$ is

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

Answer 1

The correct option is C

Positive

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

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

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

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