- 1 - 1. N TP LNG GIC 1.Cng thc cng sin( ) sin cos sin coscos( ) cos cos sin sint an t ant an( )1 t an t ana b a b b aa b a b a ba ba ba b = = = 2.Cng thc nhn == = = 2 2 2 2sin2 2si n coscos2 cos sin 1 2sin 2cos 1a a ba a a a 3.Cng thc h bc 221 cos2si n21 cos2cos2aaaa== 4.Cng thc nhn 3 22sin 3 3si n 4sincos3 4cos 3cosa a aa a a= = 5.Bin i tch thnh tng 1cos cos cos( ) cos( )21sin si n cos( ) cos( )21sin cos si n( ) sin( )21cos sin si n( ) sin( )2a b a b a ba b a b a ba b a b a ba b a b a b l= l l l= l l l= l l l= l l - 2 - 6.Bin i tng thnh tch cos cos 2cos cos2 2cos cos 2sin sin2 2sin si n 2sin cos2 2sin si n 2cos sin2 2si n( )t an t ancos coscos si n 2 sin 2 cos4 4a b a ba ba b a ba ba b a ba ba b a ba ba ba ba ba b a a = = = = = 1 1 = = ( ) ( ) 7.M rng 1sin si n sin sin 33 3 41cos cos cos cos33 3 4t an t an t an t an 33 3x x x xx x x xx x x x 1 1 = ( ) ( ) 1 1 = ( ) ( ) 1 1 = ( ) ( ) 8.Mt s php bin i c bn ( )2224 4 21 sin2 cos sin1 cos2 2cos1 cos2 2sin1sin cos 1 sin (2)211 t an t an2 cosa a aa aa aa a aaaa = = = = = 9.Bi tp 1)sin 3 3cos3 2sin2 x x x =HD: PTsin3 sin23x x 1 = =

( ) - 3 - 2) ( )2 si n 1 sin241 t ancosx xxx 1

( )= HD: PT 2(cos sin )(cos sin ) cos sin x x x x x x = = 3) 2 3 42cos 1 3cos5 5x x =HD: PT 3 26 4cos 3cos 2 05 52 3 24cos 6cos 3cos 5 05 5 5x xx x x= == = ng thc lng gic trong tam gic TrongABC ^ta c: sin( ) sincos( ) cossin cos2 2cos si n2 2A B CA C BA B CB C A = = == 1) CM:sin sin si n 4cos cos cos2 2 2A B CA B C =HD: VT2si n cos si n 2cos cos si n2 2 2 2 2A B A B C A B CC 1 = =

( )

2) CM:sin2 sin2 si n2 4si n sin sin A B C A B C = 3) CM:cos cos cos 1 4sin sin si n2 2 2A B CA B C = HD: VT 22cos cos cos 2si n cos 1 2si n2 2 2 2 2A B A B C A B CC = = 4) CM: 2 2 2cos cos cos 1 2cos cos cos A B C A B C = HD: Dng cng thc h bc - 4 - TrongABC ^khng vung ta c: t an t an t an t an t an t ant an t an t an t an t an t an 12 2 2 2 2 2cot cot cot cot cot cot 1cot cot cot cot cot cot2 2 2 2 2 2A B C A B CA B B C C AA B B C C AA B C A B C = = = = Nhn dng tam gic 1)CMR nu 2 2 2si n sin si n 2 A B c =thABC ^ vung. HD:GT

2 2 21 cos 1 cos 1 cos 22cos cos cos 0A B cA B C= == = 2)CMR nu :sin sin sin 1 cos cos cos A B C A B C = thABC ^ vung. HD:) sin sin sin 4cos cos cos2 2 2)1 cos cos cos 4si n cos cos2 2 2A B CA B CA B CA B C = = 3) Nu( )sin sin 1t an t ancos cos 2A BA BA B= thABC ^ cn. HD:

22si n cos1 si n( )2 22 cos cos2cos cos2 2cos cos si n2cos( ) 1A B A BA BGTA B A B A BCA BA B = = = == = - 5 - 2. PHNG TRNH LNG GIC I.nh ngha: L mt trong cc phng trnh sau: (1) (2) (3) (4)sincost ancotx mx mx mx m==== x l n, m l s thc cho trc. II. Cng thc nghim ca PT (1) x m sin + Nu_1 mth (1) v nghim + Nu1 m_th (1) c nghim 2sin2x kx mx k

=

= =

=

Trong l mt s thc sao chosin m =V d:233sin si n si n2 2 323x kx xx k

=

= = = =

=

Lu : 2sin sin2x kxx k

=

= =

=

( ) ( ) 2sin ( ) sin ( )( ) ( ) 2f x g x kf x g xf x g x k

=

= =

=

Nu o bng n v th 0 00 0 0.360sin180 .360x a kx mx a k

=

= =

=

- 6 - Vi1 m_trn;2 2 l l l lthsi nx m = c duy nht mt nghim. Nghim ny gi l arcsinm Khi0; 1; 1 m m m = = =th ta c cng thc nghim c bit si n 0si n 1 22si n 1 22x x kx x kx x k= = == = = = = = LUYN TP Gii cc phng trnh sau

11.1) sin221.2) si n2 sin1.3) cos2 sin21.4) cos si n 2 03 21.5) cos3 sin 3 11.6) cos 3 cos 3 13 3xx xx xx xx xx x === 1 1 = ( ) ( ) = 1 1t t = ( ) ( )

2 2 2 22 20 0 01.7) sin sin3 cos cos3cos2 31.8) cossi n cos 211.9) 3 si n coscos1.10) sin 3 cos2 1 2sin2 cos21.11) sin2 cos3 121.12) sin(2 15 ) ( 120 120 )2x x x xxxx xx xxx x x xx xx x = = = = = =