Kamren Franco

2022-01-30

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

mihady54

Beginner2022-01-31Added 13 answers

In your section where you come up with ${\alpha}_{1}+{\beta}_{2}=0$ , you have:

${\alpha}_{1}=\mathrm{sec}\left(\theta \right)+\left|\mathrm{tan}\left(\theta \right)\right|$

${\beta}_{1}=\mathrm{sec}\left(\theta \right)-\left|\mathrm{tan}\left(\theta \right)\right|$

Also we then have${\alpha}_{2}=\mathrm{sec}\left(\theta \right)+\left|\mathrm{tan}\left(\theta \right)\right|$

and${\beta}_{2}=-\mathrm{sec}\left(\theta \right)+\left|\mathrm{tan}\left(\theta \right)\right|$

So${\alpha}_{1}+{\beta}_{2}=2\left|\mathrm{tan}\left(\theta \right)\right|=-2\mathrm{tan}\left(\theta \right)$

(last equality because, as you noted, in the fourth quadrant, tangent takes on negative values).

Also we then have

and

So

(last equality because, as you noted, in the fourth quadrant, tangent takes on negative values).

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