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:
