Question

lim sin4x/sin3x
x-->0

Answer 1

find a substitute for sin(4x)

say 2sin(2x)cos(2x)

and sin(3x)

say sin(2x + x) = sin(2x)cos(x) + cos(2x)sin(x)

maybe expanding further and cancelling... to simplify...

Answer 2

here is something that may help

http://mathworld.wolfram.com/Multiple-AngleFormulas.html

Answer 3

L'Hopitals may work as well

differentiate top and bottom

\[\rightarrow \frac{4\cos(4x)}{3\cos(3x)}\]
now take limit