Solve sqrt3 csc2x=2 for all values of x.

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

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.

Find the values of the variables

Show ${\displaystyle {(\sin \left(\theta \right)-\cos \left(2\theta \right))}^2=1+\sin \left(\theta \right)-\sin \left(3\theta \right)-\frac{12}{\cos \left(2\theta \right)}+\frac{12}{\cos \left(4\theta \right)}}$

Solve the equation $\sin \theta \cot \theta =\cos \theta$

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?

if ${\displaystyle \cos 45=\frac{1}{\sqrt{2}}}$, find ${\displaystyle \cos 315,\sin 270,\sin 210,\tan 210}$