1) Sinx · tgx = Cosx + tgx 2) корень (5cosx-cos2x) = -2sinx

1) sinx * tgx = cosx + tgx;

sinx * (sinx / cosx) = cosx + sinx / cosx;

sin^2 (x) = cos^2 (x) + sinx;

sin^2 (x) = 1 - sin^2 (x) + sinx;

2sin^2 (x) - sinx - 1 = 0;

D = 1 + 4 * 2 = 9;

√D = 3;

sinx = (1 ± 3) / 4;

a) sinx = - 1/2;

x = - π/6 + 2πk; - 5π/6 + 2πk, k ∈ Z.

b) sinx = 1;

x = π/2 + 2πk, k ∈ Z.

2) √ (5cosx - cos (2x)) = - 2sinx;

{-2sinx ≥ 0;

{5cosx - cos (2x) = 4sin^2 (x);

{sinx ≤ 0;

{5cosx - 2cos^2 (x) + 1 = 4 - 4cos^2 (x);

{sinx ≤ 0;

{2cos^2 (x) + 5cosx - 3 = 0;

D = 5^2 + 4 * 2 * 3 = 49;

√D = 7;

cosx = (-5 ± 7) / 4;

a) cosx = - 3 < - 1, нет решений;

b) cosx = 1/2;

x = ±π/3 + 2πk;

{sinx ≤ 0;

{x = ±π/3 + 2πk;

x = - π/3 + 2πk.