1)Sin^2 2x+2cos^2 2x=7/4 2) вычислить 256^ log осн4 3-0,25 log осн2 3• 3^1/log осн4 9

Question

1)Sin^2 2x+2cos^2 2x=7/4
2) вычислить 256^ log осн4 3-0,25 log осн2 3• 3^1/log осн4 9

Answer 1

1)
sin²2x + 2 cos²2x = 7/4
sin²2x + cos²2x + cos²2x = 7/4
1 + cos²2x = 7/4
cos²2x = 7/4 - 1
cos²2x = 3/4
cos 2x = √3/2 или cos 2x = -√3/2

2x = π/3 + 2πn, n ∈ Z | :2
2x = -π/3 + 2πk, k ∈ Z  | :2
2x = 2π/3 + 2πn, n ∈ Z  | :2
2x = -2π/3 + 2πk, k ∈ Z  | :2

x = π/6 + πn, n ∈ Z 
x = -π/6 + πk, k ∈ Z 
x = π/3 + πn, n ∈ Z 
x = -π/3 + πk, k ∈ Z 

Или по формуле:
x = (-1)ⁿπ/6 + πn/2, n ∈ Z 
x = (-1)ⁿπ/3 + πn/2, n ∈ Z