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Question

The number of solutions of the equation cotx=cotx+1sinx in the interval 0,2π is


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Solution

Find the number of solution

Case (i): x0,π2π,3π2

cotx=cotx+1sinx, which is not possible

Case (ii): xπ2,π3π2,2π

-cotx=cotx+1sinx-2cotx=1sinx-2cosxsinx=1sinxcosx=-12x=2π3,4π3

Hence, number of solution of the equation is 2.


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