Decreasing property of ratio of two logarithmic expressions involving tangent function

Abstract

In this article, the authors review three proofs of the decreasing property of the ratio of two logarithmic expressions. With the help of the monotonicity rule for the ratio of two differentiable functions, the authors provide an alternative proof of the decreasing property of the ratio of two logarithmic expressions. These logarithmic expressions involve the tangent function.

Keywords

• Decreasing property
• logarithmic expression
• tangent function