<p>For how many values of <img alt="$x$" height="10" src="https://latex.artofproblemsolving.com/2/6/e/26eeb5258ca5099acf8fe96b2a1049c48c89a5e6.png" width="12" /> in <img alt="$[0,\pi]$" height="18" src="https://latex.artofproblemsolving.com/e/c/e/ece27ba559bd93cdf2416aa0f88fc8d7d85e5791.png" width="36" /> is <img alt="$\sin^{ - 1}(\sin 6x) = \cos^{ - 1}(\cos x)$" height="20" src="https://latex.artofproblemsolving.com/7/b/a/7bacd55a115826eb9a72c6d2c871b924bd9f11ef.png" width="216" />? Note: The functions <img alt="$\sin^{ - 1} = \arcsin$" height="16" src="https://latex.artofproblemsolving.com/3/8/5/3854566d017574445ba10fee430643e24c5be5e2.png" width="110" /> and <img alt="$\cos^{ - 1} = \arccos$" height="17" src="https://latex.artofproblemsolving.com/a/f/c/afc7390fa46f7c04c4d569d7c7ca91138bb447c9.png" width="117" /> denote inverse trigonometric functions.</p>

Question No: 288

For how many values of $x$ in $[0,\pi]$ is $\sin^{ - 1}(\sin 6x) = \cos^{ - 1}(\cos x)$ ? Note: The functions $\sin^{ - 1} = \arcsin$ and $\cos^{ - 1} = \arccos$ denote inverse trigonometric functions.

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Tags: Algebra Combinatorics

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