Question

Решите тригонометрическое уравнение
cos2x+cos3x=0

Answer 1

cos(a)+cos(b) = 2·cos(½(a+b))·cos(½(a-b))

cos2x + cos3x = 2*cos 5x/2 * cos ( -x/2) 

2*cos 5x/2 * cos ( -x/2)  = 0 
cos 2,5x  * cos ( -x/2)  = 0 

1) cos2,5x = 0 
2,5x = pi/2 + pik
x = pi/5 + (2pik)/5, k ∈ Z

2) cos( - x/2) = 0
cos (x/2)=  0
x/2 = pi/2 + pik
x = pi + 2pik, k ∈Z