Show that: [sin(2a)] / [1+cos(2a)] = tan(a)

We start by expanding out the double trigonometric terms (sin(2a)) using the double angle formula, giving us: [2sin(a)cos(a)] / [1+cos^2(a) - sin^2(a)]. Next we spot that on the denominator (bottom half of fraction) that 1 - sin^2(a) = cos^2(a), and so we can rearrange the demoninator to equal 2cos^2(a).  So now we have the expression: [2sin(a)cos(a)] / [2cos^2(a)]. When written as a fraction in vertical form (normal way rather than on screen here), we can see that we are able to cancel the constants of 2 and a cos(a) term on top and bottom, leaving us with: sin(a) / cos(a), which is equal by definition to tan(a), and so we have succeeded.