Solve the given equation 3. 2\cos^2\theta+\sin\theta=1 \ \ \ \ \ \ \ \ \

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

Solve ${\displaystyle \sqrt{3}\csc 2x=2}$ for all values of x.

Solve the equation
${\displaystyle \sin (x°-20°)=\cos 42°}$ for x, where 0 < x < 90

Given tanx is ${\displaystyle \frac{3}{4}}$. you can use the double formula to find ${\displaystyle \tan 2x}$. the teacher wants us to find 3 other doubles like ${\displaystyle \sin 2x}$ or ${\displaystyle \cos 2x}$ without using the double angle formulas.

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

How can I evaluate ${\displaystyle \underset{v\to \frac{\pi }{3}}{lim}\frac{1-2\cos v}{\sin (v-\frac{\pi }{3})}}$ without using LHospitals rule?