# lim x-->0 tan3x/tan2x = 3/2 - have to write out the algebraic steps needed to discover that this is = 3/2.I don't get math of why we break this out into (sin3x/cos3x)/(sin2x/cos2x), then times it by 1/2x and 3x, etc....just seems like there should be an easy way to think about extracting the 3/2.

Question

lim x-->0 tan3x/tan2x = 3/2 - have to write out the algebraic steps needed to discover that this is = 3/2.

I don't get math of why we break this out into (sin3x/cos3x)/(sin2x/cos2x), then times it by 1/2x and 3x, etc....just seems like there should be an easy way to think about extracting the 3/2.