Let $A,\,B$ be acute angles such that $\tan B=2015\sin A \cos A-2015\sin^2 A \tan B$.
Find the greatest possible value of $\tan B$.
This is a fun IMO problem, since it has many ways (all are nothing less than remarkable) to approach it and without any further ado, I will post with the first approach here:
$\tan B=2015\sin A \cos A-2015\sin^2 A \tan B$
$\tan B(1+2015\sin^2 A )=2015\sin A \cos A$
Showing posts with label minimum or inflexion. Show all posts
Showing posts with label minimum or inflexion. Show all posts
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