its important........?

Question

in maths,topic of limits....

we know,,if limit x->0 tanx/x=1
sinx/x=1
cosx/x=1 if limit x tends to zero
my question is this ,is that possible
cotx/x=1
cosecx/x=1
secx/x=1 iff limit x tends to zero

Answer 1

let's see:

cotx / x = 1/ xtanx = x/ x² tanx = (x / tanx) (1/x²)
limx->0 (x / tanx) (1/x²) = (1) (∞) = ∞

cosecx / x = 1 / x sinx = x / x² sinx = (x / sinx) (1/x²)
limx->0 (x / sinx) (1/x²) = (1)((∞) = ∞

secx / x = 1 / x cosx = x / x² cosx = (x / cosx) (1/x²)
limx->0 (x / cosx) (1/x²) = (1)((∞) = ∞

Answer 2

just evaluate the derivitives of the co-functions. This will tell you.