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

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Question 1135274: solve: x + tan (x) = 0 on [π/2 , π ]
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
.
The plot is below:



    graph%28+330%2C+330%2C+-1.5%2C+3.2%2C+-5.5%2C+5.5%2C%0D%0A++++++++++x%2Btan%28x%29%0D%0A%29


        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.