Question

The converse of sinx=0,x=0is

Answer 1

Step-by-step explanation:

first prove that for x>0 small that sinx<x<tanx. Then, dividing by x you get

sinx

x

<1

and rearranging 1<

tanx

x

=

sinx

xcosx

cosx<

sinx

x

.

Taking x→0+ you apply the squeeze theorem. For x<0 and small use that sin(−x)=−sinx so that

sin(−x)

−x

=

sinx

x

.