Question 653218: If tan(x)= 1/cot(x), is tan^-1 (x)= 1/cot^-1 (x)? Why or why not?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! If tan(x)= 1/cot(x), is tan^-1 (x)= 1/cot^-1 (x)? Why or why not?
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tan(x)= 1/cot(x) is true because the value one function is a reciprocal of the value of the other function.
For example, tan 30º=1/√3=√3/3
1/cot 30º=1/√3=√3/3
..
The inverses, however, are angles.
Using values for the inverses from the previous example:
tan^-1 (√3/3)=30º
1/cot^-1 (√3/3)=1/30º≠30º
Values of reciprocal functions are equal, but their inverses are not.
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