How do you solve $cot^2x - tan^2x = 0$ ?

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May 2, 2015

Solution

$cot^2x-tan^2x = 0$
$y = tan x; 1/y =cot x$
$1/y^2-y^2 =0$
$y^4-1 = 0$
$(y^2+1)(y^2-1)=0$
$y^2 = +- 1$
If $y^2 = 1$ then $tan x = +-1$
$y^2 = -1$ does not have real solution. But in terms of imaginary parts we have $tan x = +-i$

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