Is the given equation an identity?

$\(\cot\)^2x\(\cos\)^2x=\(\cot\)^2x+\(\sin\)^2x-1$

Write the following trigonometric expression in terms of the indicated function.

(tan x + cot x)/sec x; sin x

Determine the exact value of the expression using the provided data. 

tan β/2 where sec β = -4, π/2 < β < π

Which of the following expressions is equivalent to $\(\tan\)^2x$?

Determine the exact value of the given trigonometric expression using the half-angle identity.

$\(\sin\]\frac{x}{2}\)$ if $\(\cos\) x=-\(\frac{17}{21}\)$ where $\(\frac{\pi}{2}\)<x<\(\pi\)$

Determine the exact value of $\(\sin\[\left\)(\(\frac{A}{2}\]\right\))$ if $\(\cos\) A=-\(\frac{8}{15}\)$ and $90^{\(\circ\)}<A<180^{\(\circ\)}$.

Is the given equation an identity?

$\frac{2\sin \theta }{\sin 2\theta }=\frac{1}{2{\cos }^2\left(\frac{\theta }{2}\right)-1}$