Trivial Trigonometry Question, Need Help Understanding Concept

I have my final tommorow and I don't understand the concept of how to do these problems. Here are sample problems and the answers, I just don't know how to go about solving these, I tried the book, my notes, and nothing works. I know it's easy, even the book says it's easy, I just can't figure it out. I have everything else down pretty much for the final except this.

I will use sqrt(expression) to indicate the square root of whatever, keyboard needs a square root key hehe

I understand how to do like this...

cos[arctan(sqrt3)] becomes cos(pi/3) and then 1/2 is the answer

But when it's a value that I don't recognize, like 1/3, I get totally blown away. Here are two I can't figure out how to do.

**cos[2arcsin(1/3)]** .... The answer is 7/9 but I don't know how to get there I get stuck right at the beginning, trying to figure out the arcsin of 1/3. If I could figure that out I could do the rest probably. I was thinking of maybe incorporating an identity for this one because cos2x = 1 - 2sin^2x but I don't think it's needed?

Also this one

**tan[arcsin(2/5)]** .... The answer is 2/sqrt21, but why?

I can't use a decimal answer for these, any help would be great.