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#