Trng THPT Hng VngBi tp Ton khi 11 PHN I. I S V GII TCHI. CC CNG THC LNG GIC KHNG TH NO QUN1. Hai cung i nhau: -x v xcos( ) cossin( ) sintan( ) tancot( ) cotx xx xx xx x 2. Hai cung b nhau: x v xsin( ) sincos( ) costan( ) tancot( ) cotx xx xx xx x 3. Hai cung ph nhau: 2xv xsin cos cos sin2 2tan cot cot tan2 2x x x xx x x x _ _ , , _ _ , ,4. Hai cung hn km nhau Pi: x + v xsin( ) sincos( ) costan( ) tancot( ) cotx xx xx xx x+ + + + 5. Cc hng ng thc lng gic2 2221. sin cos 1 . 1 tancos1. 1 cot . tan .cot 1sina x x b xxc x d x xx+ + + 6.Cng thc cng lng giccos( ) cos .cos sin .sincos( ) cos .cos sin .sinsin( ) sin .cos sin .cossin( ) sin .cos sin .cosx y x y x yx y x y x yx y x y y xx y x y y x ++ + +7. Cng thc nhn i2 2 2 2sin 2 2sin cos : sin 2sin cos2 2cos 2 cos sin 2cos 1 1 2sinnx nxx x x TQ nxx x x x x 8. Cng thc nhn ba:3 3sin3 3sin 4sin cos3 4cos 3cos x x x x x x 9. Cng thc h bc:2 21 cos 2 1 cos 2sin cos2 2x xx x + 10. Cng thc bin i tch thnh tng[ ][ ][ ]1cos .cos cos( ) cos( )21sin .sin cos( ) cos( )21sin .cos sin( ) sin( )2x y x y x yx y x y x yx y x y x y + + + + +11 . Cng thc bin i tng thnh tchNguyn Hu Hiu - GV Trng THPT Hng Vng- TX ng Xoi-Bnh Phc 1Trng THPT Hng VngBi tp Ton khi 11 cos cos 2cos cos2 2cos cos 2sin sin2 2sin sin 2sin cos2 2sin sin 2cos sin2 2x y x yx yx y x yx yx y x yx yx y x yx y+ + + + + + A. CNG THC BIN II/. GI TR LNG GICBi 1:Cho 3 3sin < < .Tnh cos ,tan ,cot .5 2 pa p a a a a =- Bi 2:Cho 5cosa + 4 = 0 ( )o o180 < a < 270.Tnh sina , tana, cota.Bi 3:Cho o o o otan15 2 3. Tnh sin15 , cos15 , cot15 . = -Bi 4:Tnh tan x cot xAtan x cot x+=- bit 1sinx =.3 Tnh 2sin x 3cos xB3sin x 2cos x+=- bit tanx = -2Tnh 2 22sin x 3sin xcos x 2cos xC1 4sin x+ -=+ bit cotx = -3Bi 5:Chng minh: 4 4 2 2 6 6 2 2a/sin x+cos x=1-2sin xcos x;b/sin x+cos x=1- 3sin xcos x (s dng nh 1 cng thc) 2 2 2 2 2 2c/tan x = sin x+sin x.tan x; d/sin x.tanx +cos x.cotx + 2sinx.cosx = tanx + cotxBi 6:Chng minh cc ng thc sau:

2 22 2 22 2 21-2cos x 1+sin x cosx 1a/= tan x-cot x;b/= 1+2tan x;c/ +tanx= 1+sinx cosx sin x.cos x 1-sin xsinx 1+cosx 2 1-sinx cosx sinx+cosx-1 cosxd/ +=; e/=; f/= 1+cosx sinx sinx cosx 1+sinx sinx-cosx+1 1+sin x1+cosxg/( ) ( )2 22 2 2 222 2 2 21-cosx 4cotx sin x cos x - =;h/1-- = sinx.cosx;1-cosx 1+cosx sinx 1+cotx 1+tanx1 tan x-tan y sin x-sin yi/ 1-cosx 1+cot x = ;j/ =1+cosx tan x.tan y sin x.sin yBi 7:*Chng minh cc biu thc sau c lp i vi x: ( ) ( ) ( ) ( )( ) ( ) ( ) ( )6 6 4 4 4 2 4 224 4 2 2 8 8 8 8 6 6 46 64 2 4 24 4A=2 sin x+cos x -3 sin x+cos x ; B=cos x 2cos x-3 +sin x 2sin x-3C=2 sin x+cos x+sin xcos x - sin x+cos x ; D=3 si n x-cos x +4 cos x-2sin x +6sin xsin x+cos x-1E= sin x+4cos x+ cos x+4sin x; F= ; sin x+cos x-14 46 6 42 2sin x+3cos x-1 G=sin x+cos x+3cos x-1H=cosx 1-sinx 1-cosx 1-sin x +sinx 1-cosx 1-sin x 1-cos x ;(x 0; )2p II/. GI TR LNG GIC CA CUNG C BIT* Bit 1 HSLG khc:Bi 1:Cho sinx = - 0,96 vi3x 22pp < < a/ Tnh cosx ;b/ Tnh( ) ( ) sin x , cos x , tan x , cot 3 x2 2p pp p + - + - Nguyn Hu Hiu - GV Trng THPT Hng Vng- TX ng Xoi-Bnh Phc 2Trng THPT Hng VngBi tp Ton khi 11 Bi 2: Tnh:

( )( )( )( ) ( )( )2cos sin tan2 2A 2cos ; cot sin23 3sin tan sin cot2 2 2 2B cot cot tan3 cos 2 tancos cot2p pa a p aapa p ap p p pa b b ab b bp p b p ap a b - + - = - + - + + - + = - + - - - - - Bi 3:n gin biu thc: ( ) ( )( )( ) ( )9 5A sin 13 cos cot 12 tan ;2 27 3 3B cos 15 sin tan .cot2 2 25 9 7C sin 7 cos cot 3 tan 2tan2 2 2p pp a a p a ap p pp a a a ap p pp a a p a a a = + - - + - + - = - + - - + - = + + - - - + - + - Bi 4:n gin biu thc:

( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( )o o o o oA sin a sin 2 a sin 3 a ... sin 100 aB cos 1710 x 2sin x 2250 cos x 900 2sin 720 x cos 540 xp p p p = + + + + + + + += - - - + + + - + -Bi 5:n gin biu thc:

( ) ( )( )( )o oo o o19tan x .cos 36 x .sin x 52sin 2550 cos 1881 2A B9tan 368 2cos 638 cos 98sin x .cos x 992pp ppp - - -- = = + + - - Bi 6:Chng minh:

( ) ( ) ( ) ( )( ) ( )o o o o o o2 2a / sin825 cos 2535 cos75 sin 555 tan 695 tan 245 085 3b/ sin x cos 207 x sin 33 x sin x 12 2p pp p- + - + = + + + + + + - = Bi 7: Cho tam gic ABC.Chng minh:

A B Ca / sin(A B) sinA; b/ cosA cos(B C) 0; c/ sin co s ;2 23A B Cd/ cosC cos(A B 2C) 0; e/ sinA cos 02++ = + + = =+ ++ + + = + =III/. CNG THC LNG GICBi 8:Tnh gi tr cc HSLG ca cc cung sau: o o o o o15 , 75 ,105 , 285 , 3045Bi 9:Tnh gi tr cc HSLG ca cc cung sau: 7 13 19 103 299, , , ,12 12 12 12 12p p p p pBi 10: Tnh cos x3p - bit 12 3sinx , ( < x < 2 )13 2pp =-Bi 11: Cho 2 gc nhn , ab c 1 1tan , tan2 3a b = = .a/ Tnh( ) tan a b + b/ Tnh a b +Bi 12: Cho 2 gc nhn x v y tho : x y4tan x.tan y 3 2 2p+ == -a/ Tnh( ) tan x y ;tanx tany + + b/ Tnh tanx , tanyc/ Tnh x v y.Nguyn Hu Hiu - GV Trng THPT Hng Vng- TX ng Xoi-Bnh Phc 3Trng THPT Hng VngBi tp Ton khi 11 Bi 13: Tnh tan x4p - bit 40sin x41=-v 3< x