x = arctg (1 + √ 2) + Пк, к ∈ z и x = arctg (1 - √ 2) + Пк, к ∈ z
Объяснение:
cos(2x) - 4 sin(x) cos(x) + 3sin(2x) = 0
1 - sin(x)^2 - 4 sin(x) cos(x) + 3*2 sinx cosx = 0
sin(x)^2 - 2 sin(x) cos(x) - 1 = 0
Делим на cos (x)^2
tg(x)^2 - 2 tg(x) - 1 = 0
Пусть tg(x) = t, тогда
t^2 - 2t - 1 = 0
По теореме Виета
t1 + t2 = -b = 2
t1 * t2 = c = -1
t1 = 1 + √ 2
t2 = 1 - √ 2
tg(x) = 1 + √ 2 и tg(x) = 1 - √ 2
x = arctg (1 + √ 2) + Пк, к ∈ z и x = arctg (1 - √ 2) + Пк, к ∈ z
Объяснение:
cos(2x) - 4 sin(x) cos(x) + 3sin(2x) = 0
1 - sin(x)^2 - 4 sin(x) cos(x) + 3*2 sinx cosx = 0
sin(x)^2 - 2 sin(x) cos(x) - 1 = 0
Делим на cos (x)^2
tg(x)^2 - 2 tg(x) - 1 = 0
Пусть tg(x) = t, тогда
t^2 - 2t - 1 = 0
По теореме Виета
t1 + t2 = -b = 2
t1 * t2 = c = -1
t1 = 1 + √ 2
t2 = 1 - √ 2
tg(x) = 1 + √ 2 и tg(x) = 1 - √ 2
x = arctg (1 + √ 2) + Пк, к ∈ z и x = arctg (1 - √ 2) + Пк, к ∈ z