1) sin945 - tg45= -√2 - 1 = -√2 - 2
2 2
sin945=sin(360*2+225)=sin225=sin(180+45)=-sin45=-√2
2
2) ctgx=2cosx
cosx - 2cosx=0
sinx
cosx-2cosx sinx =0
sinx
sinx≠0
x≠πn
cosx-2cosx sinx=0
cosx(1-2sinx)=0
cosx=0 1-2sinx=0
x=π/2 +πn -2sinx=-1
sinx=1/2
x=(-1)^n * π/6 +2πn
Ответ: π/2 +πn;
(-1)^n * π/6 + 2πn
3) sin2x - sin3x=0
2 sin 2x-3x cos 2x+3x =0
2 2
sin (-x/2) cos 2.5x =0
-sin(x/2) cos 2.5x=0
sin (x/2) =0 cos 2.5x=0
x/2 =πn 2.5x=π/2 + πn
x=2πn x=(π/2) : (5/2) + πn : (5/2)
x=π/5 + 2πn
5
x=π/5 (1+2n)
Ответ: 2πn;
π/5 (1+2n)