(sen2a)/(1+cos2a)=tan a?

Question

Check the identity (With all the steps please)
I'll give 10 points to the clearest answer

Answer 1

sin 2a / (1 + cos 2a)

(2 sin a cos a) / (1 + (2 cos ^2 a - 1) )

2 sin a cos a / (2 cos ^2 a)

sin a / cos a

tan a

Answer 2

sin(2a) = 2sin(a)cos(a), cos(2a) = cos(a)^2 - sin(a)^2, and 1 = cos(a)^2 + sin(a)^2. Therefore: sin(2a)/(1+cos(2a)) = 2 sin(a)cos(a)/(cos(a)^2 + sin(a)^2 + cos(a)^2 - sin(a)^2) = 2sin(a)cos(a)/(2cos(a)^2) = tan(a).