Question

Помогите решить 11sin2x-7cos2x=11

Answer 1

22SinxCosx -7(Cos²x - Sin²x) = 11*1
22SinxCosx - 7Cos²x + 7Sin²x = 11*(Sin²x + Cos²x)
22SinxCosx - 7Cos²x + 7Sin²x = 11Sin²x + 11Cos²x
22SinxCosx - 7Cos²x + 7Sin²x - 11Sin²x -11 Cos²x = 0
22SinxCosx -18Cosx -4Sin²x = 0
11SinxCosx -9Cos²x -2Sin²x = 0 | :Cos²x ≠ 0
11tgx -9 -2tg²x = 0
tgx = e
2y² -11y +9 = 0
D = b² - 4ac = 121 - 72 = 49
y₁ =(11+7)/4 = 18/4=9/2=4,5
у₂ = (11-7)/4 = 1
а) у₁ = 4,5
tgx = 4,5
x = arctg4,5 + πk , k ∈Z
б) у₂ = 1
tgx = 1
x = π/4 + πn , n ∈ Z