I have the following question:Given a polynom p ( x ) I need to prove the the equation tan ⁡ x = p ( x ) has at least one solution.I defined the difference as a function f ( x ) = tan ⁡ x − p ( x ) and I know that f ( x ) is continues in any interval where tan ⁡ x is defined, so I am trying to use the Intermediate value theorem, but I don't know how.

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I have the following question:Given a polynom   p  (  x  ) I need to prove the the equation   tan  ⁡  x  =  p  (  x  ) has at least one solution.I defined the difference as a function   f  (  x  )  =  tan  ⁡  x  −  p  (  x  ) and I know that   f  (  x  ) is continues in any interval where   tan  ⁡  x is defined, so I am trying to use the Intermediate value theorem, but I don&#039;t know how.

RormFrure6h1 · Accepted Answer

Consider  g  (  x  )  =  cos  ⁡  x    p  (  x  )  −  sin  ⁡  xWe have   g  (  −  π      /    2  )  =  1 and   g  (  π      /    2  )  =  −  1. Hence   g  (      x    0    )  =  0 for a point       x    0    ,   −  π      /    2  &amp;lt;      x    0    &amp;lt;  π      /    2. Thus  p  (      x    0    )  =                    sin        ⁡                  x          0                            cos        ⁡                  x          0                      =  tan  ⁡      x    0

I have the following question: Given a polynom p <mo stretchy="false">( x <mo stretc

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