cos 3x + cos x =0 просвет [-П2;П2]и 2 sin в

1)  cos3x + cosx = 0
2cos(3x + x)/2*cos(3x - x)/2 = 0
cos2x * cosx = 0
a)  cos2x = 0
2x = /2 + n, nZ
x = /4 + n/2, n Z
n = - 1
x = /4 - /2 = - /4  [- /2;/2]
n = - 2
x = /4 -  = - 3/4  [- /2;/2]
n = 0
x = /4  [- /2;/2]
n = 1
x = /4 + /2 = 3/4  [- /2;/2]
n = 2 
/4 +  = 5/4  [- /2;/2]
Ответ: - /4;  /4
b)  cosx = 0
x = /2 + k, kZ
k = - 1
x = /2 -  = - /2  [- /2;/2]
k = 0
x = /2   [- /2;/2]
k = 1
x = /2 +  = 3/2   [- /2;/2]
Ответ: - /2; /2 

2) 2sin x - sin2x = cos2x
2sinx - 2sinxcosx - (2cosx - 1) = 0
2sinx - 2sinxcosx - 2cosx + sinx + cosx = 0
3sinx - 2sinxcosx cosx = 0    / разделяем на cosx