JEE PYQ

[JEE Advanced 1997] for 0 a i pi prove sin a 1 sin a n n sin

VAVidaara Admin Asked 2d ago 0 views 1 answer

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 · 2d ago ▲ 0

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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