Question #b852b

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Answer 1 · 2016-11-04T00:33:38

$lim_(x->0) (sinx - tanx)/(sinx + tanx) = 0$

Let's see what we can do with identities to simplify the function before evaluating.

$=lim_(x->0) (sinx - sinx/cosx)/(sinx + sinx/cosx)$

$=lim_(x->0) ((sinxcosx - sinx)/cosx)/((sinxcosx + sinx)/cosx)$

$=lim_(x->0) (sinxcosx- sinx)/cosx xx cosx/(sinxcosx + sinx)$

$=lim_(x->0) (sinx(cosx - 1))/cosx xx cosx/(sinx(cosx + 1))$

$=lim_(x->0)(cosx - 1)/(cosx +1)$

We can now substitute:

$= (cos(0) - 1)/(cos(0) + 1)$

$=0/2$

$=0$

Hopefully this helps!