tan x sin? x + sin x cos x sin x - cos X cos x - 2 cos x We begin on the right side of the equation by factoring the numerator and denominator. We can then use a Pythagorean Identity in the denominator and reduce. We can then use the ratio identity, and then factor the denominator. Finally we simplify by reducing the common factor. sin x(sin x + cos x) sin? x + sin x cos x sin (x) cos x - 2 cos x Cos sin x(sin x + cos x) (sin? x + cos? x) - cos (x) – sin²(x) = COS sin x + cos x sin x sin? x - cos (x) coS X sin x + cOS X cos²(x) = tan x . sin? x - CoS sin x + cos X = tan x: sin(x) + cos (x) (sin x - co x) tan x sin x - cos X

The relationship between the cone's vertex angle, 0, and the Mach number, M, of an aircraft that is flying faster than the speed of sound is given by 0 1 sin 2 M If 0= determine the Mach speed, M, of the aircraft. π 6' Express the speed as an exact value. M = (Simplify your answer. Type an exact answer, using radicals as needed. Rationalize the denominator.) Express the speed as a decimal to the nearest tenth. Ma Q Search (DELL IJ b