You can check out step by step proof here:
http://www.symbolab.com/solutions/proving_identities?query=Prove%20%5Cfrac%7B1%2B%5Csin%5Cleft(2%CE%B1%5Cright)%7D%7B1%2B%5Ccos%5Cleft(2%CE%B1%5Cright)%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Cleft(1%2B%5Ctan%5Cleft(%CE%B1%5Cright)%5Cright)%5E%7B2%7D