Question

which of the following is equivalent to $sec x cdot sin x cdot \tan(-x)$?
$-\tan^2 x$
$-cot^2 x$
$cot^2 x$
$-1$

Explanation:

Step1: Rewrite sec and odd tan

$\sec x = \frac{1}{\cos x}$, $\tan(-x) = -\tan x$
Expression becomes: $\frac{1}{\cos x} \cdot \sin x \cdot (-\tan x)$

Step2: Simplify first two terms

$\frac{\sin x}{\cos x} = \tan x$
Expression becomes: $\tan x \cdot (-\tan x)$

Step3: Multiply the terms

$-\tan x \cdot \tan x = -\tan^2 x$

Answer:

$-\tan^2 x$