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If cos^(-1)(cos x)=(n-x)/n,xge0, has sev...

If `cos^(-1)(cos x)=(n-x)/n,xge0`, has seven roots, then find values of n.

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Given equation is `cos^(-1)(cos x)=(n-x)/n,xge0`
or `cos^(-1)(cos x)=1-x/n,xge0`
For seven roots of equatio, the graphs of `y=cos^(-1)(cos s)" and "y=1-x/n` intersect seven times.

For seven roots, the line `y=1-x/n` must meet the x-intercept is between `6pi" and "8pi`.
`:. n in (6pi, 8pi)`
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