Question

what is cos(arcsin(1/x)+arctan(2x)) as an algebraic expression?

Answer 1

who cares

Answer 2

@natdomfio , first expand the angle sum. use cos(a+b)=cos(a)cos(b)-sin(a)sin(b)

Answer 3

Next, you want to use your inverse trigonometric identities in order to rewrite the expression wihtout trigonometric functions.

Answer 4

then I get\[\cos (\sin^{-1} (\frac{ 1 }{ x }))\cos(\tan^{-1} (2x))-\sin (\sin^{-1} (\frac{ 1 }{ x }))-\sin (\tan^{-1} (2x))\]

Answer 5

now is when you need to know your inverse trigonometric identities.
I don't, but wikipedia does.
http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Compositions_of_trig_and_inverse_trig_functions

Answer 6

You have a typo by the way.
\(\large \cos (\sin^{-1} (\frac{ 1 }{ x }))\cos(\tan^{-1} (2x))-\sin (\sin^{-1} (\frac{ 1 }{ x }))\sin (\tan^{-1} (2x))\)