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?

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