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The sum of roots of the equation cos^(-1...

The sum of roots of the equation `cos^(-1)(cosx)=[x],[dot]` denotes the greatest integer function, is (a)`2pi+3` (b) `pi+3` (c) `pi-3` (d) 2`pi-3`

Text Solution

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We have `cos^(-1)(cos x)=[x]`
To find the roods of the equation, we draw the graphs of `y=cos^(-1)(cos x)" and "y = [x]` and then find the points of intersection.

From the graph, roots are 0, 1, 2, 3, and the value ot x for which `3=2pi-x or x= 2 pi-3`. Hence the sum of roots is `2pi+3`
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