Inverse Trigonometry Identities?

Question

Please help solve and explain the problems for me.

tan(2 arctan x)

cos(2 arcsin x)

Answer 1

arctan x = u
tan u = x
tan(2 arctan x) = tan (2u)
= 2tan(u)/(1-tan^2(u))
= 2x/(1-x^2)

arcsin x = u
sin u = x
cos(2 arcsin x)
= cos (2u)
= 1 - 2sin^2 u
= 1 - 2x^2

Answer 2

tan(2 arctan x) = 2x/(1 - x^2)

cos(2 arcsin x) = 1 - 2x^2

Answer 3

The answer gudspeling gave is correct, the website below shows more of the identities, neatly shown

http://www.clarku.edu/~djoyce/trig/identities.html