apologies in advance, i'm quite new to these forums and don't know how to illustrate my question the proper way. i'll state my steps clearly and what i did in each step in brackets next to the equation.

$\displaystyle Cos pi/8 =$

(Using double angle formula $\displaystyle cos(2x) =2cos^2(x) -1$)

$\displaystyle Cos\frac{Pi}{4} = 2cos^2\frac{Pi}{8} -1$

$\displaystyle sqrt(2)/2 = 2cos^2(Pi/8) -1 $ (figured out the value of $\displaystyle cos pi/4$)

$\displaystyle sqrt(2)/2 +1 = 2cos^2(Pi/8)$ (Moved the -1 to the left, making +1)

$\displaystyle sqrt(2)/4 + 1/2 = cos^2(Pi/8)$ (Divided both sides by 2)

$\displaystyle sqrt(sqrt(2)/4 + 1/2) = cos(Pi/8)$ (Square root of both sides)

$\displaystyle cos(pi/8) = Sqrt(Sqrt(2) + 2)/2 $

seem correct? havn't got the answers in the back of my book. Seems right to me but i have to be sure i can use this method in my test. Would i be able to use this method for Tan, Sin, Cos and their recipricols?