Asked by Kramer

sin(5x)/sin(4x) = ?
How do I cancel them out to get a constant?
Answered by bobpursley
sin(5x)=sin(4x+x)=2sin4xsinx
Answered by Kramer
what property is this? in terms of a and b?
Answered by Reiny
not true Bob,

sin(4x+x)sin4x = (sin4xcosx + cos4xsinx)sin4x
= cosx + cos4xsinx/sin4x

now sin4x = sin(3x+x) = sin3xcosx + cos3xsinx
and cos4x = cos3xcosx - sin3xsinx)

now in your list of trig expansions you might have seen:
sin3x = 3sinx - 4sin^3 x
cos3x = 4cos^3 x - 3cosx

now if you have the patience to plug all that back into the above, you will have a great mess
but all expressed in x.
Don't really know what you wanted here.

Answered by Reiny
sin(4x+x)sin4x = (sin4xcosx + cos4xsinx)sin4x
should have been:

sin(4x+x) / sin4x = (sin4xcosx + cos4xsinx) / sin4x