Determine whether the given identity is true or false. 

cot(-x)cosx = sinx -cscx

Write the given trigonometric function in terms of $\cos x$.

$\tan x$

Write the following trigonometric expression in terms of sine and cosine. Express your answer in terms of $x$ only.

${\csc }^{2}x(1-{\sec }^{2}x)$

Determine the value(s) of the given trigonometric expression if $\sin x=\frac{1}{3}$.

$\frac{\sec x-\cos x}{\cos x}$

Simplify the given trigonometric expression.

$\frac{\tan x}{\sin x}+\frac{\cot x}{\cos x}$

Is the given equation an identity?

$\cos^2x\left(1+\tan^2x\right)-1=0$

Is the given equation an identity?

$\frac{1}{\csc x-\cot x}=\csc x+\tan x$