3.a) sin2x=
√3 22x = (-1)^n arcsin
√3 +πn 22x=(-1)^n
π + πn 3x=(-1)^n *
π +
πn 6 2б) √2 cos²x + cosx=0cosx (√2 cosx + 1) =0cosx=0 √2 cosx +1=0x=2πn √2 cosx=-1 cosx =
-1 √2 cosx =
-√2 2 x=
+ arccos (
-√2) + 2πn 2 x=
+ (π -
π) + 2πn 4 x=
+ 3π + 2πn 4Ответ: 2πn;
+ 3π + 2πn 4в) sinx + cosx =0cos(
π - x) + cosx =0 22 cos
π/2 -x+x cos
π/2-x-x =0 2 22 cos π/4 cos (π/4 - x) =02 *
√2 cos(-(x - π/4)) =0 2cos (x - π/4) =0x - π/4 = π/2 + πnx = π/2 + π/4 + πnx=
3π + πn 4Ответ:
3π + πn 4г) sin²x + 6 cos²x + 7sinx cosx=0
sin²x +
7 sinx cosx +
6 cos²x =
0 cos²x cos²x cos²x cos²xtg²x + 7tgx + 6 = 0Пусть tgx=yy²+7y+6=0D=49-24=25y₁=
-7-5 = -6 2y₂=
-7+5 = -1 2При у=-6tgx=-6x=π - arctg 6 + πnПри у=-1tgx=-1x=π - arctg 1 + πnx=π - π/4 + πnx=
3π + πn 4Ответ: π - arctg 6 + πn;
3π + πn 44.{x+y=π{sinx + siny = -√3x=π-ysin(π-y) + siny = -√3siny + siny = -√32 siny=-√3siny= -
√3 2y=(-1)^(n+1) *
π + πn 3x=π -πn - (-1)^(n+1) *
π 3