Prove that (tanx)(sin2x) = 2 – 2cos^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.

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

Use an expression for $\frac{\sin (5\theta )}{\sin (\theta )}$ to find the roots of the equation $x^4-3x^2+1=0$ in trigonometric form

sinh(x-y)=Sinhx*coshy-sinhy**coshx

Solve the trignometric equation $2\sin (3x+\pi /4)=\sqrt{1+8\sin 2x{\cos }^{2}x}$

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

If $A,B,C\in \mathbb{R}$ and ${\displaystyle \cos (A-B)+\cos (B-C)+\cos (C-A)=-\frac{3}{2},}$, Then
${\displaystyle \frac{\sum {\cos }^3(\theta +A)}{\prod \cos (\theta +A)},}$ , Where $\theta \in \mathbb{R}$