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The last step in a problem of mine is to find all solutions between 0 and pi/2 of the following equation:

R(tanx + 1/cosx + x - 1) = 1/2R

By simple inspection and with the aid of a graphing calculator, its obvious that the only solution is x=0, regardless of the value of R. This is enough for the assignment, but Im wondering if theres a way to mathematically isolate x and prove that 0 is the only solution

R(tanx + 1/cosx + x - 1) = 1/2R

^{2}(tanx - x)By simple inspection and with the aid of a graphing calculator, its obvious that the only solution is x=0, regardless of the value of R. This is enough for the assignment, but Im wondering if theres a way to mathematically isolate x and prove that 0 is the only solution

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