Из данных уравнений выбрать и записать в столбик уравнения с одной переменной:
2х=4, Зх-4=5х, 4х-2=у, 2х=3у, х2 +5х-3=0,
Зх-12=4, х3 =8, х2 -у=5, х+у=1, ху+2=1.

Упростите  (cos(22°-α)-cos(18°+α))²+(cos(68°-α)+sin(72°-α))²

Объяснение:           информация для размышления

sin(90 -α) =cosα  ; cos(90-α) = sinα ; cos(α-β)=cosα*cosβ+sinα*sinβ

(A ± B)² =A²±2A*B +B)²

!?  

1.  (cos(22°-α) - cos(18°+α))²+(cos(68°- α)+sin(72°-α))² =

(cos(22°-α)- cos(18°+α))²+(cos(90° -(22°+α))+sin(90°-(18°+a))² =

(cos(22°-α)- cos(18°+α))²+(sin(22°+α)+cos(18°+a) )² =

cos²(22°-α)- 2cos(22°-α)*cos(18°+α)+cos²(18°+α) +

sin²(22°+α)+2sin(22°+α)*cos(18°+a)+ cos²(18°+a)  =

!!  

2. (cos(22°-α) - cos(18°+α))²+(cos(68°+ α)+cos(72°-α))² =

(cos(22°-α)- cos(18°+α))²+(cos(90° -(22°-α))+cos(90°-(18°+α))² =

(cos(22°-α)- cos(18°+α))²+(sin(22°-α)+sin(18°+α) )² =

cos²(22°-α)- 2cos(22°-α)*cos(18°+α)+ cos²(18°+α) +

sin²(22°-α)+2sin(22°- α)*sin(18°+α) + sin²(18°+α)  =

( cos²(22°-α)+sin²(22°-α)) -2(cos(22°-α)*cos(18°+α)- sin(22°- α)*sin(18°+a) )+

( cos²(18°+α) +sin²(18°+a) ) =1 -2cos(22-α+18+α) +1 =2 -2cos40°=

2(1 -cos40°) =2*2sin²20° = 4sin²20 .

! ! !

3.  (cos(32°-α) - cos(28°+α))²+(cos(58°+ α)+cos(62°-α))² =

(cos(32°-α)- cos(28°+α))²+(cos(90° -(32°-α))+cos(90°-(28°+α))² =

(cos(32°-α)- cos(28°+α))²+(sin(32°-α)+sin(28°+α) )² =

cos²(32°-α) - 2cos(32°-α)*cos(28°+α)+ cos²(28°+α) +

sin²(32°-α) + 2sin(32°- α)*sin(28°+α)  + sin²(28°+α)  =

( cos²(32°-α)+sin²(32°-α)) -2(cos(32°-α)*cos28°+α)- sin(32°- α)*sin(28°+a) )+

( cos²(28°+α) +sin²(18°+a) ) =1 -2cos(32-α+28+α) + 1 = 2 -2cos60°=

2-2*1/2= 1

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

2(1 -cos60°) =2*2sin²30° =4sin²30 = 4*(1/2)²  =4*1/4 =1

1) 5log b^2/a (a^2/b); если log a (b)=3

                                       log a  (a^2/b)        log a (a^2) - log a (b)
5log (b^2)/a (a^2/b)= 5·  = 5·  =
                                       log a  (b^2)/a        log a (b^2)-log a (a)  
       2- 3          (-1)
= 5  = 5 = -1
       2·3 -1         5

2) log 2 (a^1/3) , если log 4 (a^3)=9

log 4 (a^3)=9  ⇔3 log 4 (a)=9 ⇔ log 4 (a)=3

                        log 4 (a^1/3)    (1/3)log 4 (a)      1log 2 (a^1/3) = = = = 2
                         log 4 (2)           log 4 (√4)          1/2

3) lg2.5 если log 4(125) = a

log 4(125) = a   ⇔ log 4(5³) =3 log 4(5) =a  ⇔ log 4(5)=a/3
            log 4 (5/2)     log 4 (5)-log 4 (2)       a/3-1/2      2a-3lg2.5 = =   =  =
            log 4 (5·2)      log 4 (5) +log 4 (2)    a/3 +1/2    2a+3