solve the multiple-angle equation. tan 3x - 1 = 0

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 ${\displaystyle \tan (x-\frac{y}{2})}$

What does x equal when ${\displaystyle \cos \left(x\right)=0}$?

Write the complex number in standard form.
$5+\sqrt{-36}$

Solve $(\sin x+\cos x)(\sin x+\cos x)$

Prove: $\csc a+\cot a=\cot \frac{a}{2}$
All I have right now, from trig identities, is
$\frac{1}{\sin a}+\frac{1}{\tan a}=\frac{1}{\tan (a/2)}$
Where do I go from there?

Prove that
${\displaystyle {\sin }^2(\frac{\pi }{8}+\frac{x}{2})-{\sin }^2(\frac{\pi }{8}-\frac{x}{2})=\frac{1}{\sqrt{2}}\sin x}$