solve: cos(5x) + sin(x) = 0
I have that:
(sin(3x) + cos(3x))(cos(2x) - sin(2x)) = 0
therefore:
sin(3x) = -cos(3x) and cos(2x) = sin(2x)
from here I'm stuck... any help would be much appreciated
Cos 5x + sin x = 0
OR
cos 5x + cos ( π/2- x )=0 [cos ( π/2- x )=sinx ]
2 cos (5x+ π/2- x )/2 cos (5x-( π/2- x ) )/2=0
[ Because cos C + cos D = 2 cos (C+D)/2 cos (C-D)/2]
That gives
2 cos (4x+ π/2 )/2 cos (6x- π/2 )/2=0
Now from here you can solve the equation.