How do you find the exact value of cot (arctan (5/8))cot(arctan(58))?

1 Answer
mason m
Mar 24, 2016

8/585

Explanation:

Recall that cot(x)=1/tan(x)cot(x)=1tan(x). Thus,

cot(arctan(5/8))=1/tan(arctan(5/8))cot(arctan(58))=1tan(arctan(58))

tan(x)tan(x) ard arctan(x)arctan(x) are inverse functions, so tan(arctan(x))=xtan(arctan(x))=x and tan(arctan(5/8))=5/8tan(arctan(58))=58.

So, we obtain:

1/tan(arctan(5/8))=1/(5/8)=8/51tan(arctan(58))=158=85

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