Simplify Cos(arctan(x))

Question

anonymous · Answer

Can Someone help I have no idea how to do this

anonymous · Answer

hmm. i dont see a way to simplify it but you could do arctan=1/tan
making it cos/tan

anonymous · Answer

seems like a waste of time to me though

anonymous · Answer

The answer is 1/sqrt(1+x^2)

anonymous · Answer

but i have no clue how to get it

anonymous · Answer

hmmmmmmmmmmm. interesting @nincompoop

anonymous · Answer

@bibby

anonymous · Answer

anonymous · Answer

that problem is a little different from yours. and that is weird.

anonymous · Answer

Yeah there are some other ones that also say to set y= tan or whaterver but after that they dont really explain where the rest comes from

anonymous · Answer

i dont see how theyre using a pythagorean identity or even a tangent out of a cosine

anonymous · Answer

starting with let y = arctan(x)

dumbcow · Answer

cos  = 1/sec = 1/sqrt(1 + tan^2)

tan(arctan x) = x

--> 1/sqrt(1+x^2)

anonymous · Answer

$$y = \arctan x$$$$\tan y = x$$|dw:1391084901690:dw|$$\cos y = \frac{1}{\sqrt{1+x^2}}$$$$\cos (\arctan x)=\frac{1}{\sqrt{1+x^2}}$$