11b. tan(510 - 219) = tan(309) =- 12. a. tan(x + n) = - tan x +tan n = tan x 1-tan x tan n b. cos(x+y) cos xcos y-sin x siny = cosy sin x sin y _ = 1 - tan(x) tan(y) cos x cos } Cos x cosy cos x cosy c. cos(x + y) cos(x - y) = (cos x cosy - sin x sin y) (cos x cosy + sin x sin y) = cos? x cos? y - sin? x sin? y 13. a. tan(20 + 20) = tan(40) b. tan(20 + 20) = tan(40) 14. a. sin(15) b. |sin(50)| 1 +V2 15. a. cot (=) 1 1+cos( = 2+v2 sin[= VZ VZ = V2+1 tan- 1-cos(=] V3 15b. sin 2-V3 V2-V3 2 +since 16. 7 cos(6x) cos(7x) = 7 * =[cos(6x + 7x) + cos(6x - 7x)] = = [cos(13x) + cos(-x)] = =[cos(13x) + cos(x)] 17. sin(2x) - sin(7x) = 2 cos () sin ) = 2 cos () sin (-x) = -2 cos sin ) 18. 3 sin (37.5) cos(7.50) = 3 * = [sin(37.50 + 7.50) + sin(37.50 - 750)] = = + } = =(VZ+1) 19. cos () - cos = -2 sin 12 12 sin 12 12 = -2 sin (#) sin (-") = 2+ 12+4=12 20. sin(6x) = 2 sin(3x) cos(3x) 21. 2 tan x 1+tan2 x - = tan(2x) 22. Period = frequency -seconds - B = - Period -,d(t) = 2.3 cos(1900nt) 950 23a. maximum = 2500 + 500 = 3000 predators 23b. Period = 21 = = n years. Every n years the predator population repeats.