Prove frac{cos(a)}{1+sin(a)}+(1+sin)

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

Verify the identity
${\displaystyle \tan \times {\csc }^{2}x–\tan x=\cot }$

Find the exact value of the expression.
$\tan {25}^{\circ }+\tan {110}^{\circ }/1-\tan {25}^{\circ }\cdot \tan {110}^{\circ }$

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

Find a double angle formula for ${\displaystyle \sec \left(2x\right)}$ in terms of only ${\displaystyle \csc \left(x\right)}$ and ${\displaystyle \sec \left(x\right)}$.

Find the general solution to ${\displaystyle \cos 2x=-\cos x}$