Luonggiac-Chuong7 - C HNG VII P HNG TRNH L N G GIA C CH A...

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CHÖÔNG VII PHÖÔNG TRÌNH LÖÔÏNG GIAÙC CHÖÙA CAÊN VAØ PHÖÔNG TRÌNH LÖÔÏNG GIAÙC CHÖÙA GIAÙ TRÒ TUYEÄT ÑOÁI A) PHÖÔNG TRÌNH LÖÔÏNG GIAÙC CHÖÙA CAÊN Caùch giaûi : AÙp duïng caùc coâng thöùc A 0B AB 0 A BA ≥≥ ⎧⎧ =⇔ ⎨⎨ B = = ⎩⎩ 2 B0 A B = Ghi chuù : Do theo phöông trình chænh lyù ñaõ boû phaàn baát phöông trình löôïng giaùc neân ta xöû lyù ñieàu kieän B baèng phöông phaùp thöû laïi vaø chuùng toâi boû 0 caùc baøi toaùn quaù phöùc taïp. Baøi 138 : Giaûi phöông trình ( ) 5cos x cos2x 2sin x 0 * −+= () * 2sin x ⇔− = 2 sin x 0 4sin x −= ( 22 sin x 0 5cosx 2cos x 1 4 1 cos x −− = ) = 2 sin x 0 3 0 +− sin x 0 1 cosx 3 loa ïi 2 =∨ = π =± + π π ⇔= −+ π∈ ± ± sin x 0 xk 2 , k 3 2 , k 3 Baøi 139 333 3 s i nx c o sx s i nx c o tg x c o sx t g x 2 s i n2 x ++ + =
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Ñieàu kieän : cos x 0 sin 2x 0 sin x 0 sin 2x 0 sin 2x 0 sin 2x 0 ≠⇔ > ⎨⎨ Luùc ñoù : () 332 2 * s i nxc o sxs i nx c o s xc o sx s i n x 2 s i n 2 x ⇔++ + = ( ) 22 sin x sin x cos x cos x cos x sin x 2sin 2x ⇔+ ++ = ( ) sin x cos x sin x cos x 2sin 2x + = 2 sin x cos x 0 sin x cos x 2sin 2x +≥ += sin x 0 2sin x 0 4 4 sin2x 1 nha än do sin2x 0 1 sin 2x 2sin 2x ⎧π ⎛⎞ ⎪⎪ ⎜⎟ ⇔⇔ ⎝⎠ = > ππ π =+ π∈ π ∨= + π ⎩⎩ ±± sin x 0 sin x 0 44 5 xk , k xm 2 x m 2 l o a ï i , m 4 π ⇔=+ π ∈ ± 2 , m 4 Baøi 140 : Giaûi phöông trình π 2 1 8 sin 2x.cos 2x 2 sin 3x * 4 + Ta coù : (*) sin 3x 0 4 1 8sin 2x cos 2x 4 sin 3x 4 ⎪⎝ π + π = + sin 3x 0 4 14 s i n 2 x1c o s 4 x 21c o s ( 6 x ) 2 ( sin 3x 0 4 1 4 sin 2x 2 sin 6x sin 2x 2 1 sin 6x = + ) = = +π ∨ = +π ∈ ± sin 3x 0 sin 3x 0 15 sin 2x x k x k , k 21 2 1 2
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So laïi vôùi ñieàu kieän sin 3x 0 4 π ⎛⎞ + ⎜⎟ ⎝⎠ Khi x k thì 12 π •= + π sin 3x sin 3k cos k 42 ππ += + π = π () ( ) = ⎢ 1 , neáu k chaün nhaän 1, neáu k leû loaïi π + π 5 Khi x k thì 12 π + π = + π 3 sin 3x sin 3k sin k 2 ( ) = 1, neáu k chaün loaïi 1, neáu k leû nhaän Do ñoù =+π =+ + π ± 5 *x m 2 x 2 m 1 , m 12 12 Baøi 141 : Giaûi phöông trình 1s i n 2 x 1s i n 2 x 4cosx * sin x −+ + = Luùc ñoù : * 1 sin 2x 1 sin 2x 2sin 2x ⇔− ++ = ( hieån nhieân sinx = 0 khoâng laø nghieäm , vì sinx =0 thì VT = 2, VP = 0 ) 22 2 2 1 sin 2x 4sin 2x sin 2x 0 +− = 1 sin 2x 2sin 2x 1 sin 2x 0 −= 242 2 1 sin 2x 4sin 2x 1 1 sin 2x 2 sin 2x 0 ⇔≥ + sin 2x 4 sin 2x 3 0 1 sin 2x 2 =∨ = 33 sin 2x sin 2x 2 sin 2x 2 3 sin 2x 2 ⇔=
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ππ = = ± 2 2x k2 2x k2 , k 33 ⇔ = +π ∨ = +π ∈ ± xk , k 63
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Luonggiac-Chuong7 - C HNG VII P HNG TRNH L N G GIA C CH A...

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