I need help deriving this function:
g(t)=tan^-1 (t/ sqrt(2 - t^2))
Any help would be appreciated! Thanks
What I got when I tried deriving it:
1/(1+(t/sqrt(2-t^2))^2) x (sqrt(2-t^2)+(t^2/(sqrt(2-t^2)))/(sqrt(2-t^2))
and eventually ended up with:
2/((sqrt(2-t^2))^3 + t^3(sqrt(2-t^2)))
Yes, I know that... can be also written as
which by trigonmetric identities , I just did not want to state something and be wrong.
Table of Trigonometric Identities
Also it is whatever choice maybe the simplest because can be written as and from your problem above
And from here you can just use a trig. substitution using the identity, that fits the description of what's under the square root.