?
, .
sin x = a; cos x = a; tg x = a; ctg x = a,
x - , 
( sin x cos x |a| < 1)
( ), :
I a > 0
Þ 
II a < 0
Þ 
III ( = 0, 1, 1)
Þ 
Þ 
Þ 
: 
; 
a sinx + b cosx = 0, a ≠ 0, b ≠ 0
.
a sin2x + b sinx cosx + c cos2x = 0,
a ≠ 0, b ≠ 0, c ≠ 0
.
:
:
a sin2x + b sinx cosx + c cos2x = 0
cos2x
( , ..: sinx cosx )
tg2x + b tgx + c = 0
(, ).
, cosx ( sinx). cos2x ( sin2x).
1. :
:
sinx cosx.
, 
,
: 
2.
3 sin2x 4 sinx cosx + cos2x = 0
.. cos2x ≠ 0,
3tg2x 4 tgx + 1 = 0 : tgx = .
32 4 + 1 = 0
D = 16 12 = 4
y1 = 1 y2 = 1/3
tgx = 1 tgx = 1/3
tgx = 1: Þ x = arctg (1/3) + πn, n ∈Z.
tgx = 1/3: Þ = arctg1 + πn, x = π/4 + πn, n ∈Z.
3.
sin2x 10 sinx cosx + 21cos2x = 0
.. cos2x ≠ 0,
tg2x 10 tgx + 21 = 0 : tgx = .
2 10 + 21 = 0
1 = 7 2 = 3
tgx = 7 tgx = 3
tgx = 7: = arctg7 + πn, n ∈Z
tgx = 3: = arctg3 + πn, n ∈Z
4
sin22x 6 sin2x cos2x + 5cos22x = 0
.. cos22x ≠ 0,
3tg22x 6tg2x +5 = 0
: tg2x =
32 6 + 5 = 0
D = 36 20 = 16
1= 5 2 = 1
tg2x = 5 tg2x = 1
tg2x = 5: 2 = arctg5 + πn, = 1/2 arctg5 + π/2 n, n ∈Z
tg2x = 1: 2 = arctg1 + πn = π/8 + π/2 n, n ∈Z
5
6sin2x + 4 sin(π-x) cos(2π-x) = 1.
|
|
|
6sin2x + 4 sinx cosx = 1.
6sin2x + 4 sinx cosx sin2x cos2x = 0.
5sin2x + 4 sinx cosx cos2x = 0.
.. cos2x ≠0, 5tg2x + 4 tgx 1 = 0
: tg x = .
52 + 4 1 = 0
D = 16 + 20 = 36
1 = 1/5 2 = 1
tg x = 1/5 tg x = 1
tg x = 1/5: = arctg1/5 + πn, n ∈Z
tg x = 1: = arctg(1) + πn, n ∈Z
= π/4 + πn, n ∈Z
7
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