Kamren Franco

## Answered question

2022-01-30

A basic doubt while taking square roots of variables which have $±$ sign before the square root sign.

### Answer & Explanation

mihady54

Beginner2022-01-31Added 13 answers

In your section where you come up with ${\alpha }_{1}+{\beta }_{2}=0$, you have:
${\alpha }_{1}=\mathrm{sec}\left(\theta \right)+|\mathrm{tan}\left(\theta \right)|$
${\beta }_{1}=\mathrm{sec}\left(\theta \right)-|\mathrm{tan}\left(\theta \right)|$
Also we then have ${\alpha }_{2}=\mathrm{sec}\left(\theta \right)+|\mathrm{tan}\left(\theta \right)|$
and ${\beta }_{2}=-\mathrm{sec}\left(\theta \right)+|\mathrm{tan}\left(\theta \right)|$
So ${\alpha }_{1}+{\beta }_{2}=2|\mathrm{tan}\left(\theta \right)|=-2\mathrm{tan}\left(\theta \right)$
(last equality because, as you noted, in the fourth quadrant, tangent takes on negative values).

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