Question

Помогите решить Cos4X - SinX =0

Answer 1

Cos(a+b) - sin (a-b) = (cosb + sinb)(cosa - sina)  
a = 5/2   b = 3/2  ->  cos4x - sinx = 
(cos3/2x + sin3/2x)(cos5/2x - sin5/2x) =0 ->
cos3/2x + sin3/2x = 0 -> tg3/2x = -1  -> 3/2x = - π/4 + πn
-> x = - π/6 +2πn/3
cos5/2x - sin5/2x = 0 -> tg5/2x = 1  -> 5/2x = π/4 + πn ->
x = π/10 + 2πn/5