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2011 AIME I Problems/Problem 9

Revision as of 11:45, 19 March 2011 by AlphaMath1 (talk | contribs) (→‎Problem)

Problem

Suppose $x$ is in the interval $[0, \pi/2]$ and $\log_(24\sin x) (24\cos x)=\frac{3}{2}$. Find $24\cot^2 x$.

Solution

We can rewrite the given expression as $\sqrt{24^3\sin^3 x}=24\cos x$. Square both sides and divide by $24^2$ to get $24\sin ^3 x=\cos ^2 x$

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