Verifying Trigonometric Identities

I have been having lots of trouble verifying trigonometric identities. I know the fundamental identities but I am actually having trouble with the algebra that goes along with the problems.
The problem I am working on now is:

cos(x)-tan(x)/sin(x)cos(x) = csc^2 (x) - sec^2 (x)

(The csc and sec are squared. I didn't know the best way to right that on here)

I tried to change everything to sin/cos but I felt like I made the equation much more confusing doing that.

I got:

(cos(x)/sin(x))-(sin(x)/cos(x))/(sin(x)cos(x)) = (1/sin(x))^2 - (1/cos(x))^2

I am more than a little lost.

I also tried it by changing only the left side and got:

(cot(x)-tan(x)) (1/sin(x)) (1/cos(x))

With either option I don't know where to go next and I'm not even sure if I started correctly.

eumyang
Homework Helper
I have been having lots of trouble verifying trigonometric identities. I know the fundamental identities but I am actually having trouble with the algebra that goes along with the problems.
The problem I am working on now is:

cos(x)-tan(x)/sin(x)cos(x) = csc^2 (x) - sec^2 (x)

(The csc and sec are squared. I didn't know the best way to right that on here)
Looks like you have a typo there, because as written the LHS won't simplify to the RHS. I think you mean this:
$$\frac{\cot x - \tan x}{\sin x \cos x} = \csc^2 x - \sec^2 x$$

(Also, "right" should be "write".)

In which case, why don't you start by splitting the LHS into a difference of 2 fractions and go from there.

I feel silly for writing "write" as "right". There was a typo. Thank you for figuring that out and for the tip!