please anser the question in image

lim x tends to 0 sinmx/tannx

please answer these too

limx→0tanxsinx=1

Plugging in 0 right away yields tan(0)sin(0)=00, an indeterminate form, so we must simplify.

Recall tanx=sinxcosx.

So,

limx→0tanxsinx=limx→0sinxcosxsinx=limx→0sinxcosxsinx=limx→0secx=sec0=1