Solvecos 30° cos 35° - sin 30° sin 35°

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.

Finding all a such that ${\displaystyle f\left(x\right)=\sin 2x-8(a+1)\sin x+(4a^2+8a-14)x}$ is increasing and has no critical points
Obviously, the first thing I did was to find the derivative of this function and simplify it a bit and I got:
${\displaystyle f^{\prime }\left(x\right)=4({\cos }^{2}x-2(a+1)\cos x+(a^2+2a-4))}$
But now how do I proceed further, had it been a simple quadratic in x.

How to prove ${\displaystyle \frac{e^{jx}-j{e}^{-jx}}{j{e}^{jx}-e^{-jx}}=\frac{\tan x-1}{\tan x+1}}$
where ${\displaystyle j=\sqrt{-1}}$
Ive

${\displaystyle (\sin x+\cos x)²=1+\sin 2x}$

What is ${\displaystyle \cos 135}$?

Solve: ${\displaystyle 4\sin (2y-0.3)+5\cos (2y-0.3)=0}$