Find the general solution: 1-tan^2(x)/1+tan^2(x)=1-2sin^2(x)

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

Find $\theta$ from the equation $\cos \theta \cdot \cos 2\theta \cdot \cos 3\theta =1/4$

Veronica made a triangle by taking an 8 1/2 × 11 sheet of paper and putting a dot at the top. She then drew lines from the bottom corners to the dot and cut along the lines (see diagram).
[Triangles]
What is the area of the triangle that Veronica cut out?

${\displaystyle \frac{\tan \alpha +\cot \alpha }{\sin \alpha -\cos \alpha }={\sec }^2\alpha +{\csc }^2\alpha }$

For an acute angle A , can cos A be larger than 1? Explain the answer.

Hypotenuse = 5cm, need to work out opposite. (angle opposite the opposite is 34 degrees)