(sinx+tanx)/1+secx=sinx

First, the numerator:

(sinx+tanx) = (sinx + sinx/cosx) = (sinx) (1+(1/cosx)) = (sinx) (1+secx)

The denominator (of the left side of equation) is (1+secx)

The (1+secx) on the top and the (1+sec x) on the bottom cancel out.

You are left with sinx = sinx.

-Andy