What trig identity did they use?

[quickclick330]

Hi I'm having trouble understanding how they simplified this integration using trig substitutions...I really don't know what identities they used to make these substitutions or the strategy behind why this substitution was made(particularly the 3 steps in the red box). Obviously it works but I just can't click into place why...thanks for the help!

 

[ircdan]

double angle formula, sin(2x) = 2sinxcosx