Shafqat K.

asked • 05/01/16

prove that tan^-1(-x)=-tan^-1(x)

just prove

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Kenneth S. answered • 05/01/16

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This is equivalent to saying that tangent function is an odd function, which is a fact.
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Mark M.

NOT REALLY!
A function is an odd function iff -f(x) = f(-x). And, as you say, -tan(x) = tan(-x).
YET
The problem IS NOT about the tangent function, rather about the inverse (arctan, tan-1) of the tangent function.
The inverse of a function may or MAY NOT be a function! E.g., the inverse of the sine function is a function only over a restricted domain.
NOTHING can be assumed about the parity of a function based on the parity of its inverse.
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05/01/16

Kenneth S.

Newsflash: Arctan function is defined such that the output (range) is (-pi/2,pi/2).  This is a well known fact, i.e. that's why your calculator gives you one answer for arctan(z)...a value in Quadrant IV when z < 0, otherwise a value in Quadrant I.
 
 
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05/01/16

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