One algorithm for testing annulling of mixed trigonometric polynomial functions on boundary points

This paper considers one problem of automated proving of MTP inequalities f(x) > 0 over [0, π/2] on boundary points. It suggests one algorithm for symbolic checking for f(0) = 0 or $f\left( {\frac{\pi }{2}} \right) = 0$ without use of numerical estimations. With stated approach it gives one contribution to theory and practice in this part of the field of automated proving.