Question

use the trigonometric identities to write the expression in terms of a single trigonometric identity or a constant. tan(x) sec(x) sin(x) sin²(x) tan²(x) 1 cos²(x)

Explanation:

Step1: Substitute trigonometric identities

Recall that \(\tan(x)=\frac{\sin(x)}{\cos(x)}\) and \(\sec(x)=\frac{1}{\cos(x)}\).
So, \(\tan(x)\sec(x)\sin(x)=\frac{\sin(x)}{\cos(x)}\cdot\frac{1}{\cos(x)}\cdot\sin(x)\)

Step2: Simplify the expression

$$
LATEXBLOCK0
$$

Answer:

\(\tan^{2}(x)\) (the second option)