# Math Help - Trig Functions

1. ## Trig Functions

I was wondering if someone could please take a look at my numbers 12 and 21...I need to simplify them so that the right and left sides are equal...but I am stuck on these final two problems...could anyone please assist me?

2. Hello, aikenfan!

$12)\;\frac{\cot^3\!x}{\csc t} \:=\:\cos t(\csc^2\!t - 1)$
We have: . $\frac{\cot t}{\csc t}\cdot\cot^2\!t \;\;=\;\;\frac{\dfrac{\cos t}{\sin t}}{\dfrac{1}{\sin t}} \cdot\cot^2\!t \;\;=\;\;\cos t\cot^2\!t \;\;=\;\;\cos t(\csc^2\!t - 1)$

$21)\;\csc x - \cos x \:=\:\sin x\tan x$
This one has a typo . . . It is not true.

It's probably: . ${\color{blue}\sec x} - \cos x \:=\:\sin x\tan x$

On the left: . $\frac{1}{\cos x} - \cos x \;\;=\;\;\frac{1-\cos^2\!x}{\cos x} \;\;=\;\;\frac{\sin^2\!x}{\cos x} \;\;=\; \;\sin x\cdot\frac{\sin x}{\cos x} \;\;=\;\;\sin x\tan x$