How do you evaluate #tan(arctan(10))#?

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Answer 1 · 2017-01-25T13:06:40

#tan(arctan(10))=10#

Because #arctan(x)=tan^(-1)(x)#, we can see that #tan(x)# and #arctan(x)# are inverses of each other.

Remember that #f(f^(-1)(x))=x#

In this case, replace #f# with #tan# and #x# with #10#.

Then we get

#tan(tan^(-1)(10))=tan(arctan(10))=10#

Answer 2 · 2017-01-25T13:27:57

10

#tan(arctan(10)#

#:.=tan(84.28940656)#

#:.=10#