Prove that the following identity is true. sec y – tan y = 1 sec? y + tan? y We begin on the left side of the equation by factoring the numerator. We can then reduce and, using a Pythagorean Identity, simplify. sect y – tant y- (sec? y sec? y + tan? y )(sec? + tan? y) sec? y + tan? y sec? = 1

The amount of time in seconds it takes for a swimmer to hear a single, hand-held, starting signal is given by the formula below, where (x,y) is the location of the starter (in meters), (0,p) is the location of the swimmer (in meters), and C is the air temperature (in degrees Celsius). Assume that the starter is located at the point (4,-2). Answer parts a and b below. t(x,y.p.C) = √²+(y-p)² 331.45+0.6C a. Calculate t(4, -2,30,20) and t(4, -2,20,20). Could the difference in time change the outcome of a race? t(4, -2,30,20) = (Round to five decimal places as needed.) Ay p Swimmer Starter (4,-2) P

B. For number 4, perform the division and simplify. 1-sec x 4. 1+sec x 5 tan x 10 tan? x