N1
(2cosx - 1) × корень из sinx = 0
2cosx = 1 sinx = 0
cosx = 0,5 x = πk, k € Z
x = +- π/3 + 2πn, n € Z
ответ : x = +- π/3 + 2πn, n € Z ; πk, k € Z
N2
3sin^2 (x) - 4sinx × cosx + 5cos^2 (x) = 2
3sin^2 (x) - 4sinx × cosx + 5cos^2 (x) - 2 = 0
-2 = -2sin^2 (x) - 2cos^2 (x)
sin^2 (x) - 4sinx × cosx + 3cos^2 (x) = 0
tg^2 (x) - 4tgx + 3 = 0
tgx = 1 tgx = 3
x = π/4 + πn x = arctg(3) + πk
ответ : π/4 + πn, n€ Z; arctg(3) + πk, k€ Z
N3
4^x - 2^x - 12 < 0
2^2x - 2^x - 12 = 0
2^x = t
t^2 - t - 12 = 0
t = 4
t = -3
2^x = 4 2^x = -3
x = log 2 (4) = 2 x - не существует
ответ : 2
N1
(2cosx - 1) × корень из sinx = 0
2cosx = 1 sinx = 0
cosx = 0,5 x = πk, k € Z
x = +- π/3 + 2πn, n € Z
ответ : x = +- π/3 + 2πn, n € Z ; πk, k € Z
N2
3sin^2 (x) - 4sinx × cosx + 5cos^2 (x) = 2
3sin^2 (x) - 4sinx × cosx + 5cos^2 (x) - 2 = 0
-2 = -2sin^2 (x) - 2cos^2 (x)
sin^2 (x) - 4sinx × cosx + 3cos^2 (x) = 0
tg^2 (x) - 4tgx + 3 = 0
tgx = 1 tgx = 3
x = π/4 + πn x = arctg(3) + πk
ответ : π/4 + πn, n€ Z; arctg(3) + πk, k€ Z
N3
4^x - 2^x - 12 < 0
2^2x - 2^x - 12 = 0
2^x = t
t^2 - t - 12 = 0
t = 4
t = -3
2^x = 4 2^x = -3
x = log 2 (4) = 2 x - не существует
ответ : 2