# 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 $tan^{-1}tan \theta = |x|$
 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.
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 $1\neq-1$.