How to verify this identity?sin x + tan x/ 1 + sec x = sin x thank you very much!

We need to prove that :

sinx+
tanx / (1+ sec x ) = sinx

We will start from the left
side.

(sinx + tanx)/ (1+
secx)

We know that tanx = sinx/cosx ans secx =
1/cosx.

Then, we will substitute with
identities.

==> (sinx+ sinx/cosx) / (1+
1/cosx)

==> [(sinx*cosx + sinx)/cosx] / [ ( cosx +
1)/cosx]

Reduce
cosx.

==> (sinxcosx + sinx ) / (cosx +
1)

Now we will factor sinx from the
numerator.

==>
sinx*(cosx+1)/(cosx+1)

Now we will reduce
cosx+1

==>
sinx

Then we proved that (
sinx+tanx)/(1+secx) = sinx.