# Is this equation correct

by utkarshakash
Tags: correct, equation
 PF Gold P: 847 1. The problem statement, all variables and given/known data Is this equation correct for permissible values of x $tan^{-1}|tan x| = |x|$ 2. Relevant equations 3. The attempt at a solution I assume LHS to be θ. Then tanθ=|tanx| The original equation becomes $tan^{-1}tan \theta = |x|$
 Sci Advisor HW Helper Thanks P: 26,148 hi utkarshakash! (what do you mean by "permissible"? ) wouldn't it be easier to start by saying |tanx| = tan|x| ?
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,683 No, that is not correct because tangent is not a "one-to-one function". For example, if $\theta= 5\pi/4$ then $tan(\theta)= tan(5\pi/4)= 1$ so that $tan^{-1}(tan(\theta))= tan^{-1}(tan(5\pi/4))= tan^{-1}(1)= \pi/4$, not $5\pi/4$. Since everything is positive, the absolute value is irrelevant.
P: 295
Is this equation correct

 Quote by tiny-tim hi utkarshakash! (what do you mean by "permissible"? ) wouldn't it be easier to start by saying |tanx| = tan|x| ?
Even if so, it is still wrong, as tangent can be negative for positive values of x. For instance, $\tan(7\pi/4)=-1$. It is easy to observe from here that $|\tan(7\pi/4)|\neq \tan|7\pi/4|$, as $1\neq-1$.
 Homework Sci Advisor HW Helper Thanks P: 9,933 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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