Cal Question
Show that
cos(arctan(sin(arccot(x)))=sqrt{frac{x^2+1}{x^2+2}}

Question

Cal Question
Show that 
cos(arctan(sin(arccot(x)))=sqrt{frac{x^2+1}{x^2+2}}

myininaya · Answer

$$\cos(\arctan(\sin(arccot(x)))=\sqrt{\frac{x^2+1}{x^2+2}}      $$

anonymous · Answer

what are you kidding?

hero · Answer

myininaya, if I had to put money on it, I'd bet you already have this solved

myininaya · Answer

lol
this is a question in the book
i just thought it would fun

myininaya · Answer

no i was just looking and seen it and thought i would give it a try

anonymous · Answer

actually i bet i can do it without any calculus at all yes? you have an odd idea of fun

myininaya · Answer

i was thinking that satellite

anonymous · Answer

this question looks ridiculous!

myininaya · Answer

i know

hero · Answer

lol

myininaya · Answer

thats why i chose it

anonymous · Answer

oh i lied

anonymous · Answer

i thought i could just work from the inside out but i cannot.  so i guess you do ...
would you like my guess?

hero · Answer

myininaya, just post the solution already.

myininaya · Answer

i just started working on it

zarkon · Answer

actually pretty easy

anonymous · Answer

my guess is take the derivative of both sides. see that you get the same thing.  then evaluate somewhere, see that you get the same thing.  that is my guess

anonymous · Answer

i just got it.

zarkon · Answer

just make 2 right triangles

anonymous · Answer

zarkon's right, its not that bad.

anonymous · Answer

i have them on my paper. but what do you do with.. oh never mind. i am a moron

anonymous · Answer

last step is 
$$\cos(\arctan(\frac{1}{\sqrt{x^2+1}})$$ if i am not mistaken

anonymous · Answer

right.

hero · Answer

Can somebody post it on a pdf?

anonymous · Answer

i can write it out maybe, it is not bad

myininaya · Answer

easy

myininaya · Answer

attachment

anonymous · Answer

start with 
$$\sin(\tan^{-1}(x))=\frac{1}{\sqrt{x^2+1}}$$

anonymous · Answer

i gotta learn to do that.  do you scan these?

myininaya · Answer

i'm a scanner

myininaya · Answer

with a scanner

anonymous · Answer

lol

myininaya · Answer

lol

anonymous · Answer

got it. oh look some one posted a nice integral for you to do!

myininaya · Answer

i scan the hell out of things

myininaya · Answer

zarkon remember it is my favorite thing to do to make right traingles lol

anonymous · Answer

http://openstudy.com/groups/mathematics#/groups/mathematics/updates/4e4894120b8b8d00ebe06793

zarkon · Answer

yep...fun for all ages :)

anonymous · Answer

go get 'em. i'm off.

myininaya · Answer

i could give this to my trig students 
why would you want to show this using cal?

myininaya · Answer

i don't know if that is possible to use cal for this problem

zarkon · Answer

doing it once is good for trig sub...but having to do it twice..i don't see a point