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Luonggiac-Chuong9

# Luonggiac-Chuong9 - C HNG IX HE PHNG TRNH L N G GIA C I...

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CHÖÔNG IX: HEÄ PHÖÔNG TRÌNH LÖÔÏNG GIAÙC I. GIAÛI HEÄ BAÈNG PHEÙP THEÁ Baøi 173: Giaûi heä phöông trình: ( ) ( ) 2cosx 1 0 1 3 sin2x 2 2 = = Ta coù: ( ) 1 1 cosx 2 = ( ) x k2 k 3 π = ± + π Z Vôùi x k 3 2 π = + π thay vaøo (2), ta ñöôïc 2 3 sin2x sin k4 3 2 π = + π = Vôùi x 3 π = − + π k2 thay vaøo (2), ta ñöôïc 2 3 sin2x sin k4 3 2 π = + π = − 3 2 (loaïi) Do ñoù nghieäm c a heä laø: 2 , 3 π = + π ± x k k Baøi 174: Giaûi heä phöông trình: sinx siny 1 x y 3 + = π + = Caùch 1: Heä ñaõ cho x y x y 2sin .cos 1 2 2 x y 3 + = π + = π = = π π + = + = x y x y 2.sin .cos 1 cos 1 6 2 2 x y x y 3 3

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4 2 2 3 3 = π = π π π + = + = x y x y k k x y x y ( ) 2 6 2 6 π = + π π = π x k k Z y k Caùch 2: Heä ñaõ cho 3 3 3 1 sin sin 1 cos sin 1 3 2 2 3 3 sin 1 2 3 3 2 2 6 2 6 π π = = π + = + = π π = = π π π + = + = + π π = + π π = π ± y x y x x x x x y x y x x x k x k k y k Baøi 175 : Giaûi heä phöông trình: sinx siny 2 (1) cosx cosy 2 (2) + = + = Caùch 1: Heä ñaõ cho x y x y 2sin cos 2 (1) 2 2 x y x y 2cos cos 2 (2) 2 2 + = + = Laáy (1) chia cho (2) ta ñöôïc: + = x y x y tg 1 (docos 0 2 2 = khoâng laø nghieäm cuûa (1) vaø (2) ) 2 4 2 2 2 2 + π = + π π π + = + π ⇔ = + π x y k x y k y x k thay vaøo (1) ta ñöôïc: sinx sin x k2 2 2 π + + π = sinx cosx 2 + =