1、 3. x + bx + cx + d = 0 1,-1, 1 2 , c = 3 2 . 4. x - 4 = 0, x = . 2 + 7 1 2 3 4 5 0 3 2 1 = . 13. sin = 1 3 cos2 = . , 6 4 3 . 9. 22 7 , 355 113 , 3.14159265. 13. 7 9 14. 1 2 (n + 4 ). 15. 5 3 3 19. 1 5 3. cosC = 1 8 , sinC = 3 8 7, sinB = 5 16 7, sinA = 1 4 7. 4. : 2 3 165, : 2 7 385 : (0, 1155). 2
2、 21 x +1 x -1+ x -1x +1 = 10 3 3 1 1 2 4 6 7 0 5 - log 3007 + log 7003 + log 1 10 10 10 cos2x = 1 2, x x - 2xy 3y = 9, 4x - 5xy 6y = 30 2 2 2 2 (1) 12 25+ 90000 + 64 27 4 6 (2) (2x + 1 x) 3 12 k - 4 3 12= 0, k = ,k = 2 2 2 12 12 = log ( 300 7 700 3 1) = log 10000 = 4 10 10 tan870 = tan(900 - 30 ) =
3、tan(-30 ) = -tan30 = - 1 3 cos2x = 1 2 , 2x = 2n 3 ,x = n 6 = 12 + 3 + 4 = 169 = 13 2 2 2 1 2 3 4 = 6 = 1 4(3 + 4 +5)(3 + 4 -5)(3 - 4 + 5)(-3 + 4 + 5) = 6 4 3 R = 36 3 I x xy y x y II x xy y x y 2 2 2 2 2 3 9 4 0 2 3 9 2 3 0 - + = + = - + = - = x y x y 1 1 2 2 4 3 3 1 3 3 4 3 3 1 3 3 = = - = - = x y
4、 x y 3 3 4 4 3 2 3 2 = = = - = - (1) = 3 2 5 + 3 10 + 2 3= 2 5 3 +10 3 + 2 3 3= 166 153 2 2 2 4 4 6 3 6 T = C (2x ) ( 1 x ) = C 2 x r+1 12 r 3 12 r r 12 r 12 r 36 4r C C 12 9 12 9 12 3 3 2 2 1760 - = = AC sin45= 1sin75 = = + = - AC sin sin ( ) ( ) 45 75 2 2 2 2 3 2 1 2 3 1 ABC S = 1 2 1 ( 3 1) sin60
5、 = 1 4 (3 3) - - (a b ) (a b ) (b ) - 3 2 2 -1 -3 1 2 1 2 7 1 3 16 logx = 1 3 loga + 2logb + logc (3 02) , 1 1000 4 1 + tgx 1 - tgx = 1 + sin2x, x = (a b a b b )= (a b )= (a b )= a 3 2 -2 1 2 - 3 2 h 7 2 1 3 3 2 + 1 2 -2- 3 2 + 7 2 1 3 2 0 1 3 2 3 logx = loga b c1 6 1 3 2 x = a b cx = (a b c) = a b
6、c 1 6 1 3 2 1 3 2 6 2 12 6 = 1 2 ( c 2 ) = 1 2 c 4 = 1 2 a + b 4 = 1 2 ( a 2 ) + 1 2 ( b 2 ) 2 2 2 2 2 2 3a = 4r a = 2 3 3r 2 2, V = a = ( 2 33r) = 8 9 3r 3 3 3 a sin 180 - ( + r) = bsin ,b = asin sin 180 - ( + r)= asin sin( + r) (x - 7 6 ) = 1 3 (y + 61 12 ) 2 , ( 7 6 , 61 12 ) - M( 7 6 - 61 6 ,0),
7、 N( 7 6 + 61 6 ,0), M( 7 - 61 6 ,0),N( 7 + 61 6 ,0) (- , 7 - 61 6 ), (7 + 61 6 ,+ ) ( 7 - 61 6 , 7 + 61 6) OA = 1 2 (O A + O A ) = 1 2 O O 1 1 2 2 1 2 cosx + sinx cosx - sinx = (cosx + sinx) , 2 x = k - 4 k x = k - 4 , x = k k a = R(R + ) 2 R(R + h) = R + 2(R + h) , a l l R = - h , 2 2 l 2a( - h + h
8、) = a ( - h + ), (2a - a ) - h = a - 2ah. 2 2 2 2 2 2 l l l l l l (2a - a ) - ( h ) = a - 2a h 2 l l l l (4a - 4aa +a ) - ( h ) = a -4aa h + 4a ( h ) , (8a - 4aa +a )( h ) - 4aa h + (4aa -4a ) = 0 2 2 2 2 2 2 2 2 2 2 l l l l l l h l = (-4aa) - 4(8a -4aa+a )(4aa 2 2 2 -4 2 a ) h l = 4aa 16a(2a - a) 2
9、(8a - 4aa +a )= 2aa 2(2a - a ) a(2a - a ) 4a + (2a - a ) 3 2 2 2 2 cosA = AB + AC - BC 2AB AC = 16BC +16BC - BC 2 4BC 4BC= 31 32 , 2 2 2 2 2 2 cosB = cosC = CD CA = 1 2 BC 4BC = 1 8 AH = a 22,SH = a 2 2 tanx = -1 x = n - 41 2 cosx - 1 2 sinx = 1 2 , cos(x + 4 ) = cos 4 , x + 4 = 2n 4 , x = 2n 2n - 2
10、 6 6 6 6 6 ( )( ) ( ) - + - - - = x y x x y 3 ,4 37 , tan tan x + 6x + 7 = 0 , sin( + ) = cos( + ) 2 a b a b a b 7 12 136 2 2 x y x y x y + - - = + = P ABC , PA BC AB PB PC 2 2 = + BAM = 1 2 ABC ,AEF = 1 2 ABC cos = 9 +16 - 37 24 = - 1 2 , sin( + ) cos( + )= tan( + ) = tan + tan 1 tan tansin( + ) =
11、cos( + ) a b a b a b a b a b a b a b - = - - = 6 6 1 7 x + y x 2 - - = + = x y y 12 1 136 2 2 ( ) ( ) (1) (x + y) 7 x + y + 12 = 0,( x + y 3)( x + y 4) = 0,x + y = 3, x + y ) = 4. - - - ( ) x + y = 9 x( ) x + y = 16 x 2 2 + = + = y y 2 2 136 136 ( ) x + y = 9 x( ) x + y = 9 x x = 9 + 191 2 9 191 2 x = 9 191 2 9 + 191 2 1 2 - = - = - = - - = y y y y 191 191 1 2 ( ) x + y = 16 x( ) x + y = 16 x x = 10 x = 10 3 4 - = - = - = = y y y y 4 4 6 6 3 4 x = 9 + 191 2 9 191 2 x = 9 191 2 9 + 191 2 x = 10 6 x = 6 10 1 2 3 4 y y y y 1 2 2 4 = - - = = = : AB = AD AO BD.A AB =
