Luonggiac-Chuong6 - CHNG VI: PHNG TRNH ANG CAP a sin2 u + b...

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CHÖÔNG VI: PHÖÔNG TRÌNH ÑAÚNG CAÁP 22 asin u bsinucosu ccos u d ++ = Caùch giaûi : () Tìm nghieäm u k luùc ñoù cosu 0 vaø sin u 1 2 π •= + π = = ± 2 Chia hai veá phöông trình cho cos u 0 ta ñöôïc phöông trình : •≠ atg u btgu c d 1 tg u = + Ñaët ta coù phöông trình : tt g u = 2 ad t b tcd 0 −+ + = Giaûi phöông trình tìm ñöôïc t = tgu Baøi 127 : Giaûi phöông trình ( ) cos x 3 sin 2x 1 sin x * −= + Vì cosx = 0 khoâng laø nghieäm neân Chia hai veá cuûa (*) cho 2 cos 0 ta ñöôïc * 1 2 3tgx 1 tg x tg x ⇔− = + + t = tgx ta coù phöông trình : 2 2t 2 3t 0 += t0t 3 ⇔=∨= Vaäy * π ⇔= = = π = + π ± tgx 0 hay tgx 3 x k hay x k , k 3 Baøi 128 ( ) 33 2 cos x 4 sin x 3cos x sin x sin x 0 * −− + = Khi xk t h ì c o s x 0 v a ø s i n x 2 π =+ π = = ± 1 thì (*) voâ nghieäm Do khoâng laø nghieäm neân chia hai veá cuûa (*) cho cos 3 x = cos x 0 ta coù (*) ( ) 32 2 1 4tg x 3tg x tgx 1 tg x 0 + + = ⇔+− = ⇔+ = ∨= ± ππ −+π ±+π∈ ± 2 3tg x 3tg x tgx 1 0 tgx 1 3tg x 1 0 3 tgx 1 tgx 3 , k 46
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Baøi 129 : Giaûi phöông trình ( ) 42 2 4 3cos x 4sin xcos x sin x 0 * −+ = Do cosx = 0 khoâng laø nghieäm neân chia hai veá cuûa (*) cho 4 cos x 0 Ta coù : (*) 24 34 t g xt gx 0 ⇔− + = ⇔= ∨= ππ ⎛⎞ ± = ± ± ⎜⎟ ⎝⎠ ±+π ±+π∈ ± 22 tg x 1 tg x 3 tgx 1 tg tgx tg 43 xk , k Baøi 130 : Giaûi phöông trình ( ) sin 2x 2tgx 3 * += Chia hai veá cuûa (*) cho 2 cos x 0 ta ñöôïc (*) 2sinxcosx 2tgx 3 c o sx c o sx c o ⇔+ = 2 () ( ) 2tgx 2tgx 1 tg x 3 1 tg x + = + 32 tt g x 2t 3t 4t 3 0 = = = −− + 2 g x t12 t t3 0 = π ⇔=+π∈ ± tgx 1 , k 4 Baøi 131 ( ) 3 sin x sin 2x sin 3x 6cos x * 23 * 2sin x cos x 3sin x 4 sin x 6cos x = 3 ( ) •= = ± Khi cos x 0 ( sin x 1) thì * voâ nghieäm Chia hai veá phöông trình (*) cho 3 cos x 0 * 2sin x 3sinx 1 .4 cos x cos x cos x cos x +− 3 6 = + −= = = = α ± π α α = ± 3 2
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This note was uploaded on 11/26/2011 for the course MATH 1002 taught by Professor Chuck during the Spring '11 term at University of Western States.

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Luonggiac-Chuong6 - CHNG VI: PHNG TRNH ANG CAP a sin2 u + b...

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