Find all solutions of the equation in the interval [ 0 , 2 <mrow class="MJX-TeXAtom-

Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 11 passengers per minute.

If ${\displaystyle \sin x+\sin y=a\text{and}\cos x+\cos y=b}$ then find ${\displaystyle \tan (x-\frac{y}{2})}$

How to prove ${\displaystyle \frac{e^{jx}-j{e}^{-jx}}{j{e}^{jx}-e^{-jx}}=\frac{\tan x-1}{\tan x+1}}$
where ${\displaystyle j=\sqrt{-1}}$
Ive

${\displaystyle \underset{x\to \frac{\pi }{4}}{lim}\frac{({\csc }^{2}x-2{\tan }^{2}x)}{(\cot x-1)}}$ without L'Hôpitals Rule.

Solve the given equation
${\displaystyle 3.2{\cos }^2\theta +\sin \theta =14.{\sin }^2\theta =4-2{\cos }^2\theta }$
${\displaystyle 5.{\tan }^2\theta -2\sec \theta =26.{\csc }^2\theta =\cot \theta +3}$

Solve the equation $\frac{\cot (x)-\tan (x)}{({\cot }^2(x)-{\tan }^2(x)}=\sin x\cos x$

How do I evaluate the limit ${\displaystyle \underset{x\to 0}{lim}\frac{\sin 3x}{x\cos 2x}}$?
I'm having trouble doing this problem: the farthest I've gotten is just using a limit law for division and then moving the constant x in the denominator in front. I also thought about leaving ${\displaystyle \underset{x\to 0}{lim}\frac{\sin 3x}{1}}$ and then somehow introducing 3x so it turns into a special limit.
Otherwise, I'm just stuck.