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