How do you simplify this in terms of sine and cosine? (All I know is that the answer is )

First, note that

Then, to give that parenthetical part of your expression a different look, start with the Pythag ID...



... and divide everything in that identity by and see where that leads you.

Give that a go and see what happens.

Well, I would have first converted everything into sin and cos, but leaving 1 as it is. (because 1 has many definitions, we get less confused by it.)

Expanding using distributive property, we get

Then, combining both into a single fraction does the trick.

Thinking more about it, there is an even faster way.

So, expanding makes which is also sec^2x! And the definition of sec is 1/cos, so , directly 1/cos^2x.

Had to spread the rep arcsine :(