[JEE Advanced 1997] For $0<A_i<\pi$, prove $\sin A_1+\cdots+\sin A_n\le n\sin\dfrac{A_1+\cdots+A_n}n$.
For $0<A_i<\pi$, prove $\sin A_1+\cdots+\sin A_n\le n\sin\dfrac{A_1+\cdots+A_n}n$.
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 1mo ago
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Answer: Proved (Jensen's inequality).
$\sin$ is concave on $(0,\pi)$, so by Jensen the average of $\sin A_i$ is at most $\sin$ of the average, giving the inequality.
JEE Advanced 1997 · Binomial Theorem — verified solution by the Vidaara Team.
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