F(x) = cos5x · cos(x + π/6)
g(x) = sin5x · sin(x + π/6) + 0.5√3
cos5x · cos(x + π/6) = sin5x · sin(x + π/6) + 0.5√3
cos5x · cos(x + π/6) - sin5x · sin(x + π/6) = 0.5√3
cos (6x + π/6) = 0.5√3
6x + π/6 = ⁺₋ π/6 + 2πn n∈Z
1) 6x₁ + π/6 = + π/6 + 2πn n∈Z 2) 6x₂ + π/6 = - π/6 + 2πn n∈Z
1) 6x₁ = 2πn n∈Z 2) 6x₂ = - π/3 + 2πn n∈Z
1) x₁ = πn/3 n∈Z 2) x₂ = - π/18 + πn/3 n∈Z
Ответ: x₁ = πn/3 n∈Z
x₂ = - π/18 + πn/3 n∈Z
2cos^2x-2sin2x+1=0.
2cos^2x - 4sinxcosx + 1 = 0
2cos^2x - 4sinxcosx + sin^2x + cos^2x = 0
sin^2x - 4sinxcosx + 3cos^2x = 0 /: cos^2x не рав. 0
tg^2x - 4tgx +3=0
(tgx - 1 )(tgx - 3 ) = 0
1) tgx = 1 ==> x = pi/4 +pik, k c Z
2) tgx = 3 ===> x = arctg(3) +pik, k c Z
Подробнее - на Znanija.com - znanija.com/task/3818797#readmore
х км/ч - скорость лодки
(х+2) км/ч - скорость по течению, (х-2) км/ч - скорость против течения
36/(х-2)+22/(х+2)=3
36x+72+22x-44=3(x^2-4)
58x+28-3x^2+12=0
3x^2-58x-40=0
D=3364+480=62^2
x1=(58+62)/6=20 x2=(58-62)/6=-4/6
20 км/ч - скорость лодки
(5/2)^2+3.06-0.4=
25/4+3.06-0.4=
6.25+3.06-0.4=8.91
Х^-6х+5>0
Д=16;х=5;х=1
(-~;1)(5;+~)