Because (1/x) tanx = e (tanxln (1/x))

Because lim tanxln( 1/x)

=lim -xlnx (because tanx~x)

=0

So lim (1/x) tanx = e 0 =1.

(2)

Because (sinx/x) (1/x 2)

=e^(( 1/x^2)ln(sinx/x))

but

Forest (1/x 2) ln (sinx/x)

= lim( 1/x^2)(sinx/x- 1)

(because ln (sinx/x) = ln (1+(sinx/x-1))

=lim (Sinks-x)/x 3

=- 1/6 (this step can be obtained by Taylor expansion or L'H?pital's law).

So the original formula = e (- 1/6)