1)7tg x-10ctg+9=0
2)5sin2x-14cos(квадрате)x+2=0
3)9cos2x-4cos(квадрате)x=11sin2x+9

1.7 tg x – 10ctg x + 9 = 0 | * tgx

7 tg²x -10 +9tgx = 0

tgx = z

7z² + 9z -10 = 0

z₁ = -2                                        z₂ = 5/7

tgx = -2                                      tgx = 5/7

x = arctg(-2) + πk , k ∈Z             x = arctg(5/7 ) + πn , n ∈Z  

2.0sinxcosx-14cos^2(x)+2sin^2x+2cos^x=0

2sin^2х+10sinxcosx-12cos^2x=0. (:соs^2x)

2tg^2x+10tgx-12=0 (:2)

tg^2x+5tgx-6=0

tgx=t

t^2+5t-6=0

D=49

t1=1

t2=-6

tgx=1

X=П/4+Пк;к€Z

tgx=-6

X=-arctg6+Пк;к€Z

3.9 cos 2x — 4 cos^2 x — 11 sin 2x — 9 = 0

9 cos^2 x — 9 sin^2 x — 4 cos^2 x — 22 sin x cos x = 0

2 cos^2 x + 9 sin^2 x + 11 sin x cos x = 0 | разделить на cos^2 x

2 + 9 tg^2 x + 11 tg x = 0

9y^2 + 11y + 2 = 0

(y + 1)(9y + 2) = 0

tg x = y; y1 = -1, y2 = -2/9

Пошаговое объяснение: