\(...A=\dfrac{\left(cos7x+cos13x\right)+\left(cos9x+cos11x\right)}{\left(sin7x+sin13x\right)+\left(sin9x+sin11x\right)}\)
\(\Leftrightarrow A=\dfrac{2cos10xcos3x+2cos10xcosx}{2sin10xcos3x+2sin10xcosx}\)
\(\Leftrightarrow A=\dfrac{2cos10x\left(cos3x+cosx\right)}{2sin10x\left(cos3x+cosx\right)}\)
\(\Leftrightarrow A=cot10x\)