tan inverse (1/x) = cot inverse (x) - pi for x less than 0 and = cot inverse x for x greater than 0. I know how to verify this but my doubt is when I'm changing functions how do I know that for like here about 0 we've different answers so how do I know that about which value I've check and will there always be only 1 such value? I mean how can we say that below 0 answer will always will same and not change I.e. cot inv x -pi . Pls show for other function like sin cos also

Dear Student, 
It depends upon the graph, here is the graph of arc tan 1/x :

Now pay attention to the part for x<0. 
And now the graph of arc cotx is 

Now we can see that the graph for x<0 is not same but by looking at the graph of
 -π+cot-1x we can see that for x<0 the graph is same so that is why they are equal. 

Similar approach for the arc sinx, arc cosx etc. 

  • -4
  • -1
What are you looking for?