Multiply and simplify: frac{(sin theta+cos theta)(sin theta+cos theta)-1}{sin theta cos theta}

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 the following:
${\displaystyle {\tan }^{2}x+1+\tan x\sec x=1+\frac{\sin x}{{\cos }^{2}x}}$

What does x equal, if ${\displaystyle \sin \left(x\right)}$

Verify the identity ${\displaystyle \sec \theta \cot \theta -\sin \theta =\frac{{\cos }^2\theta }{\sin \theta }}$

How do I evaluate ${\displaystyle \underset{z\to 1}{lim}(1-z)\tan \frac{\pi z}{2}}$
I tried using the identity, ${\displaystyle \tan \frac{x}{2}=\frac{1-\cos x}{\sin x}}$ to simplify this to:
${\displaystyle \underset{z\to 1}{lim}(1-z)\frac{\sin \pi z}{1+\cos \pi z}}$

Find every angle theta with ${\displaystyle 0\le \theta \le 2\pi radians,and2{\sin }^2\left(\theta \right)+\cos \left(\theta \right)=2}$