Question

Which of the following expressions can be used to complete the equation below?

Answer 1

Answer:

$\tan x \sin x$

Step-by-step explanation:

$\dfrac{\sec x}{1 + \cot^2 x} =$

$= \dfrac{\frac{1}{\cos x}}{1 + \frac{\cos^2 x}{\sin^2 x}}$

$= \dfrac{\frac{1}{\cos x}}{\frac{\sin^2 x}{\sin^2 x} + \frac{\cos^2 x}{\sin^2 x}}$

$= \dfrac{\frac{1}{\cos x}}{\frac{\sin^2 x + \cos^2 x}{\sin^2 x}}$

$= \dfrac{\frac{1}{\cos x}}{\frac{1}{\sin^2 x}}$

$= \dfrac{\sin^2 x}{\cos x}}$

$= \dfrac{\sin x}{\cos x}\sin x$

$= \tan x \sin x$