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

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) ⁿ π/3 + πn/2, n ∈ Z