Solve frac{csc x(sin^{2}x+cos^{2}xtan x)}{sin x+cos 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 ${\displaystyle \tan (x-\frac{y}{2})}$

Rewrite the expression as an equivalent expression thatdoesn't contain powers of trigonometric functions greater than 1. $\cos 4x$

t is a real number and P=(x,y) is the point on the unit circlethar corresponds to t. Find the exact values of the six trigonometric functions of t.
$(\frac{1}{2},\frac{-\sqrt{3}}{2})$

Find the exact values of ${\displaystyle {\sin }^{-1}\frac{1}{2}}$.

The pentagon at the right is equilateral and equiangular.
a. What two triangles must be congruent to prove $\overline{HB}\cong \overline{HE}$?
b. Write a proof to show $\overline{HB}\cong \overline{HE}$

To further justify the Cofunction Theorem, use your calculator to find a value for the given pair of trigonometric functions. In each case, the trigonometric functions are cofunctions of one another, and the angles are complementary angles. Round your answers to four places past the decimal point.
${\displaystyle {\sec 6.7}^{\circ },\cos ec{83.3}^{\circ }}$