A2. а) cos (x/2)= - 1/2;
x/2 = + - π/3 + 2πk;
x = + - 2 π/3 + 4 πk; k∈Z.
б) sin(x + π/4) = 1/2;
x + π/4 =(-1)^(k) ·π/6 + πk;
x = (-1)^(k) ·π/6 - π/4 + πk; k∈Z.
в) cos x = 4/5;
x = + - arccos(4/5) + 2πk; k∈Z.
г) ctg x = 1/√3;
x = π/6 + πk; k∈Z.
A3.
а) tg^2 x - 3 tg x - 4 = 0;
D = 9+16 = 25 = 5^2;
tg x =4 ; x= arctg4 + πk; k∈Z.
tg x = -1; x = - π/4 + πk; k∈Z.
б) 4 sin^2 x - cos x - 1 = 0;
4( 1 - cos^2 x) - cos x - 1 = 0;
4 - 4 cos^2 x - cos x - 1 = 0;
4 cos^2 x + cos x - 3 = 0;
D = 1 + 48 = 7^2;
cos x= - 1; x = π+ 2πk; k∈Z.
cos x = 3/4; x = + - arccos(3/4) + 2πk; k∈Z.
в) cos 2x + cos^2x + sinx·cosx = 0;
cos^2 x - sin^2 x + cos^2 x + sinx·cosx= 0;
sin^2x - sinx·cosx - 2 cos^2 x= 0; /:cos^x≠0;
tg^2 x - tgx - 2 = 0;
D = 1 + 8 = 3^2;
tgx = -1; x = - π/4 + πk; k∈Z;
tg x = 2; x = arctg2 + πk; k∈Z.
A4.
sin x + cos x = √2; /:√2;
1/√2 ·sinx + 1/√2 · cos x = 1;
sin x · cos(π/4) + cos x · sin(π/4) = 1;
sin(x + π/4) = 1;
x + π/4 = π/2 + 2πk;
x = π/2 - π/4 + 2πk;
x = π/4 + 2πk; k∈Z.