Решите уравнение: cos^2 x(x+pi/3)=1

Question

Решите уравнение: cos^2 x(x+pi/3)=1

Answer 1

Sin²(x + π/3) = 1
1) sin(x + π/3)  = - 1
x + π/3 = - π/2 + 2πk, k ∈z
x = - π/3 - π/2 + 2πk, k ∈z
x = - 5π/6 + 2πk, k ∈z
2) sin(x + π/3)  = 1
 x + π/3  = π/2 + 2πn, n∈Z
 x=  - π/3  + π/2 + 2πn, n∈Z
 x=  π/6 + 2πn, n∈Z

Comments

cos²(x + π/3) = 1
1) cos(x + π/3) = - 1
x + π/3 = π + 2πk, k ∈z
x = - π/3 + π + 2πk, k ∈z
x = 2π/3 + 2πk, k ∈z
2) cos(x + π/3) = 1
x + π/3 = 2πn, n∈Z
x= - π/3 + 2πn, n∈Z

Answer 2

Cos²(x+π/3)=1
[1+cos(2x+2π/3)]/2=1
1+cos(2x+2π/3)=2
cos(2x+2π/3)=1
2x+2π/3=2πn
2x=-2π/3+2πn
x=-π/3+πn