1.
2sinx.cosx
– 3sin2x = 0
ó 2sin2x – 3sin2x = 0
ó -sin2x = 0
ó -2x = k2π
-2x = π – k2π
ó x = -k2 π/2
x = - π/2 + k2 π ( k ∈ Z).
2.
2sinx + √2sin2x = 0
ó
2sinx + √2.sinx.cosx = 0
ó
2sinx . (√2cosx +1 ) = 0
ó
2sinx = 0 hay √2cosx
+ 1 = 0
ó 2sinx
= 0 hay
√2cosx = π
ó x = k2π
hay √2x = π + k2π
x
= π + k2π hay √2x = -π + k2π
ó x
= k2π/2 hay x =
π/√2 + k2π/√2
x
= π/2 + k2 π/2 hay x = - π/√2 + k2π/√2 ( k ∈ Z).
3.
Sinx + sin2x + sin3x = 0
ó sin3x + sinx + sin2x = 0
ó 2sin (3x+x)/2 . cos (3x-x)/2 + sin2x = 0
ó 2sin2x .cosx + sin2x = 0
ó sin2x (2cosx + 1) = 0
ó sin2x = 0 hay 2cosx + 1 = 0
ó sin2x = 0 hay
cosx = -1/2
ó sin2x = 0 hay
cosx = 2π/3
ó 2x =
k2 π hay x = 2 π/3 + k2 π
2x = π + k2 π hay x = -2 π/3 + k2 π
ó x =
k2 π/2 hay x
= 2 π/3 + k2 π
x
= π/2 + k2 π/2 hay x = -2 π/3 + k2 π ( k ∈ Z).
4.
2cos4x – 2sin4x + 1 = 0
ó 2. [(cos2x)2
– (sin2x) 2 +1 = 0
ó 2.
(cos2x – sin2x).(cos2x + sin2x) + 1=
0
ó2 cos2x
. 1 + 1 = 0
ó
2cos2x + 1 = 0
ó cos2x = -1/2
ó cos2x
= 2 π/3
ó 2x = 2 π/3 + k2 π
2x =
-2 π/3 + k2 π
ó x = π/3 + k2 π/2
x = -π/3 +
k2 π ( k ∈ Z).
5.
Sin2x + cos2x = 0
ó
(sinx . cosx)2 +1/8 = 0
ó (1/2
. 2.sinxcosx)2 + 1/8 = 0
ó (1/2
. sin2x )2 + 1/8 =0
ó ¼ .
sin22x + 1/8 = 0
ó ¼ .
(1 – cos4x)/2 + 1/8 = 0
ó 1/8
.(1 – cos4x) + 1/8 = 0
ó 1/8
.(1 – cos4x) =
-1/8
ó (1
– cos4x) = -1
ó 1 – cos4x = -1
ó cos4x = -2
ó cos4x = 2 (loại)
Vì -1 ≤ cos ≤ 1
6.
Sin4x
+ √2cos2x = 0
ó
2sin2x.cos2x + √2cos2x = 0
ó
cos2x . (2sin2x +√2) = 0
ó cos2x
= 0 hay 2sin2x +√2 = 0
ó
cos2x = π/2 hay sin2x
= √2/2
ó
cos2x = π/2 hay
sin2x = - π/4
ó 2x = π/2 + k2 π hay 2x = -π/4 + k2 π
2x = -π/2
+ k2 π hay 2x = π + π/4 + k2 π
ó x = π/4 + k2 π/2
hay x = -π/8 + k2 π/2
x = -π/4
+ k2 π/2 hay x = 3π/8 + k2 π/2 ( k ∈ Z).
7.
sinx.cosx.cos2x – √3/8 = 0
ó (½.
2.sinxcosx) . cos2x - √3/8 =0
ó 1/2 .
sin2x . cos2x - √3/8 = 0
ó ½ .½
.2.sin2xcos2x -√3/8 = 0
ó ¼ .sin4x
– √3/8 = 0
ó ¼.
sin4x = √3/8
ó sin4x = √3/2
ó sin4x = π/3
ó 4x = π/3 + k2 π
4x = π – π/3 + k2 π
ó x = π/12 + k2 π/4
x = π/6 + k2 π/4 ( k ∈ Z).
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