Question

Решить уравнение

 

Cosx+2Cos2x=1

Answer 1

$[begin{array}{l} Cosx + 2Cos2x = 1\ Cosx + 2(2{cos ^2}x - 1) = 1\ cosx + 4{cos ^2}x - 2 - 1 = 0\ 4{cos ^2}x + cosx - 3 = 0\ left[ begin{array}{l} cos x = - 1\ cos x = frac{3}{4} end{array} right.left[ begin{array}{l} x = pi + 2pi n,n in z\ x = pm arccos frac{3}{4} + 2pi k,k in z end{array} right. end{array}]$