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Is this equation correct 
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#1
Jan813, 06:38 AM

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1. The problem statement, all variables and given/known data
Is this equation correct for permissible values of x [itex]tan^{1}tan x = x[/itex] 2. Relevant equations 3. The attempt at a solution I assume LHS to be θ. Then tanθ=tanx The original equation becomes [itex]tan^{1}tan \theta = x[/itex] 


#2
Jan813, 06:50 AM

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hi utkarshakash!
(what do you mean by "permissible"? ) wouldn't it be easier to start by saying tanx = tanx ? 


#3
Jan813, 06:53 AM

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No, that is not correct because tangent is not a "onetoone function". For example, if [itex]\theta= 5\pi/4[/itex] then [itex]tan(\theta)= tan(5\pi/4)= 1[/itex] so that [itex]tan^{1}(tan(\theta))= tan^{1}(tan(5\pi/4))= tan^{1}(1)= \pi/4[/itex], not [itex]5\pi/4[/itex]. Since everything is positive, the absolute value is irrelevant.



#4
Jan813, 07:41 AM

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Is this equation correct



#5
Jan913, 06:24 AM

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Thanks all for your answers.



#6
Jan913, 02:46 PM

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Another way to look at it is that atan(y) always produces a result in the range [0,pi/2). So the statement must be false for any x outside that range.



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