How do you find the exact value of $\cos(tan^{-1}sqrt{3})$ ?

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Answer 1 · 2014-11-12T15:49:36

Method 1

Let $theta=tan^{-1}sqrt{3}$ .

By rewriting in terms of tangent,

$Leftrightarrow tan theta=sqrt{3}={("Opposite")}/{("Adjacent")}$

So, we can let

$("Opposite")=sqrt{3}$ and $("Adjacent")=1$ .

By Pythagorean Theorem,

$("Hypotenuse")=sqrt{(sqrt{3})^2+1^2}=sqrt{4}=2$ .

Hence,

$cos(tan^{-1}sqrt{3})=cos theta={("Adjacent")}/{("Hypotenuse")}=1/2$

Method 2

$cos(tan^{-1}sqrt{3})=cos(pi/3)=1/2$

I hope that this was helpful

How do you find the exact value of \cos(tan^{-1}sqrt{3})\cos(tan^{-1}sqrt{3})?