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Question

If x(0,π6), then the number of solutions of the equation {2x}+{tanx}=0 is

(Here, {x} denotes the fractional part of x.)
  1. 0
  2. 3
  3. 2
  4. 1


Solution

The correct option is A 0
{2x}+{tanx}=0
Both the terms of LHS are non-negative.
So, {2x}=0     (1)
x= ...,1,12,0,12,1,32,...

and {tanx}=0     (2)
x= ...,π,0,π,...
There is no common value x(0,π6) which satisfies both (1) and (2).
For x(0,π6), there is no solution.

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