Answer: D) Tan x sin x
Step-by-step explanation:
[tex]\dfrac{sec}{1+cot^2}\\\\\\=\dfrac{1}{cos}\cdot \dfrac{1}{1+cot^2}\\\\\\=\dfrac{1}{cos}\cdot \dfrac{1}{1+(\frac{cos}{sin})^2}\\\\\\=\dfrac{1}{cos}\cdot \dfrac{1}{(\frac{sin^2}{sin^2})+(\frac{cos^2}{sin^2})}\\\\\\=\dfrac{1}{cos}\cdot \dfrac{sin^2}{sin^2+cos^2}\\\\\\=\dfrac{1}{cos}\cdot \dfrac{sin^2}{1}\\\\\\=\dfrac{sin\cdot sin}{cos\cdot 1}\\\\\\=\boxed{tan\cdot sin}[/tex]
