How do you evaluate $cot(arctan (3/5))$ ?

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Answer 1 · 2016-05-28T06:15:38

$5/3$

Let $a = arc tan (3/5)$ . Then, $tan a = 3/5$ .

So, the given expression is $cot a = 1/(tan a)=5/3$ .

Answer 2 · 2016-05-28T18:24:28

$5/3$

Use the fact that $cot(x)=1/tan(x)$ to show that

$cot(arctan(3/5))=1/tan(arctan(3/5))$

Note that $tan(x)$ and $arctan(x)$ are inverse functions—namely, $tan(arctan(x))=x$ and $arctan(tan(x))=x$ .

So, the tangent and arctangent functions in the denominator will cancel one another out, leaving only $3/5$ :

$1/tan(arctan(3/5))=1/(3/5)=5/3$

How do you evaluate cot(arctan (3/5))cot(arctan (3/5))?