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Unformatted text preview: 128 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. Chapter 3 Differentiation r=(seC\/§)tan(%) => 32(secfi)(sec -)(-81—)+tan(%)(seC\/5tan\/§ (19) : —61 sec 63cc2 (é) + *5 tan (é) sec 9121an (sec W) [In em _) — W] q = 1%) :> 99 : (s) . s w) : 1—csc (51—21)) <—-—> y = cos (63—92) : gg = — sin (€92) d1!) (6‘92) 2 (— sin (9792)) (6—62) 3‘17 {—02) = 20e’92 sin (6‘92) y z 036—29 cos 50 2> 392 (302) (6—2 9cos 50) + (193 cos 50)e 2" 510(_ 219) — 5(sin 50) (03c ‘29) 2 026—26 (3 cos 50— 20 cos 50 — 50 sin 50) 911%“ — 2 sin (711— 2)- —sin (711— 2) = 2 sin (7r: — 2) - cos (7rt — 2) - fi (711 — 2) = 271 sin (711 — 2) cos (711— 2) y = sin2 (711 — 2) :> d y : sec2 711 :> 3% :(2 sec 711) (T1 d(sec 7n) — (2 sec m)(sec m [an 7rt)- 11—: d(7rt) — 271' sec2 71: tan 711 y z (1 + cos 20-4 2 %{ : —4(1 + cos 21)-5-%(1 + cos 21) = —4(1 + cos 21)-5(—s1n 20%(21): “1+3”; y=11+cor<11> 2 :s 11: —2<1+cot(a>)3- sweets»=—2(1+coto))‘3-(was)s1 _ cscu — (l +cot(§))' y = ewszim‘l) :> % = ewszm‘ ') -2cos(7rt — 1) - (—sin(7rt — 1)) -71' : —27rsin(7rt — 1)cos(7r[ — 1)e°°sz(’"‘ 1) y : (esin(t/2))3 :> 9x : 3(esin(t/2))2 _ emu/2). cos( ,1. ). % : %C08(%)6 sin (t/2) e2sin(t/2) ~ %C05(%)C3Sin(t/2) I‘M" y : sin (cos (2t 5)):> 7 cos (cos (2t— 5))~ % cos (2t — 5) 2 cos (cos (2t — 5)) - (—sin (2t — 5)) ~ 1% (2t -— 5) = —2 cos (cos (2t — 5))(sin (2t — 5)) y z (5 sin (a) 2 Ex = on (5 (o) - s (s 511(1))— — mums» (Season s1. :-%sin (5 sin G) (COS 9) y: a 1 + cos 23(71)] 3%: g [1 + cos 22-01)] -2 cos (71)( s1n (71))(7) —7[1 + cos 2201)} (cos (7t) sm (71)) y = (1 +cos(1‘1))”2 => 9% = 2 (1 +cos(12))_1/2 . g (1 +cos(12)) : 1(1 +cos(12))‘1/2(—s1n(12) . fi (12)) = — § (1 + cos (t2))_1/2 ' (sin (12)) - 2t 2 — 3:329) ...
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