Вычислите 1)√4/25; 2)√9/121; 3)√81/225 4)√100/289 5)√5^2; 6)√0,8^2; 7)√16^2; 8)√3,24^2

Question

Алгебра: Вычислите 1)√4/25; 2)√9/121; 3)√81/225 4)√100/289 5)√5^2; 6)√0,8^2; 7)√16^2; 8)√3,24^2

MrPuk · Accepted Answer

Task/27400429

Решите sin(x+30)+cos(x+60 ) =1+cos2x

cos(x+60°)+sin(x+30°) =1+cos2x ;

cosx*cos60° - sinx*sin60° +sinx*cos30° +cosx*sin30° =1+cos2x ;
(1/2)*cosx - (√3 /2 )sinx + sinx* (√3 /2 ) +cosx*(1/2) =2cos²x ;
cosx = 2cos²x ;
2cosx (cosx -1/2)= 0  ;
cosx =0 ⇒ x =π/2+πn , n ∈Z .
или
cosx -1/2=0 ⇔cosx =1/2 ⇒ x = ±π/3 +2πk , k  ∈ Z.

ответ : π/2+πn ,n ∈Z ;  ±π/3 +2πk , k  ∈ Z.

cos(x+60°)+ cos(90° -(x+30°) ) =1+cos2x ;
cos(x+60°)  +cos(60°- x) =1+cos2x ;
2cos60°*cosx =2cos²x ;
cosx = 2cos²x ;
... дальше как в
* * * * * * * P.S. * * * * * * *
cos(α+β) =cosαcosβ - sinαsinβ ;
sin(α+β) =sinαcosβ + cosαsinβ ;
cos2x =cos²x -sin²x = 2cos²x - 1⇒1+cos2x =2cos²x ;.
cos(90° - α) =sinα
cosα+cosβ= 2cos(α+β)/2 *cos(α-β)/2 .

MOGZ ответил