If A = 40°, B = 60°, and a = 20, find b

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.

In general, tan (α + β) is not equal to tan α + tan β. However, there are some values of α and β for which they are equal. Find such α and β, and do the same for tan (α - β).

What does x equal if ${\displaystyle \sin \left(x\right)=1}$?

Can we find two non-congruent right triangles with whole-number lengths and congruent hypotenuses?

Given that $\cos \theta =-0.489$ where $\pi <\theta <3\frac{\pi }{2}$, find $\sin \theta$

If $A={40}^{\circ },B={60}^{\circ }$, and $a=20$, find b.