SOLUTION: solve: x + tan (x) = 0 on [π/2 , π ]

Question 1135274: solve: x + tan (x) = 0 on [π/2 , π ]
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
x = 0 is an obvious solution, but not within the spec'd range.
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Other solutions can be found only by using graphical or iterative methods.
Do you know how to do that?

Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

The plot is below: Plot y = x + tan(x) and it clearly shows that there is only one possible solution in the given interval near x= 2. The solution CAN NOT be obtained algebraically. The only way is to obtain an approximate solution NUMERICALLY. I used online (free of charge) solver from the site https://www.wolframalpha.com/input/?i=x+%2B+tan(x)+%3D+0 It gave me the approximate solution x= 2.02876 (only one in the given interval).

Answered and solved.

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