Some Trigonometric Inequalities

Abstract

In the book [1] one finds that almost all triangles inequalities are symmetric in form when expressed in terms of the sides a, b, c or the angles A, B, C of a given triangle. No doubt that also assymmetric triangle inequalities play a very important role in geometric inequalities. It should be noted that many of these inequalities are still valid for real numbers A, B, C which satisfy the condition $$ A + B + C = p\pi , $$ where p is a natural number (which has to be odd in some cases). This also applies to the inequality of M. S. Klamkin [2] which can be specialized in many ways to obtain numerous well known inequalities.