Let's look at the first factor and consider where:
Divide through by and so obviously :
where .
So, what is in this case?
Can you use a similar method for the first factor?
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.