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

Resolved: "A basic doubt while taking square roots of..."

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

α_{1} + β_{2} = 0

, you have:

α_{1} = \sec (θ) + | \tan (θ) |

β_{1} = \sec (θ) - | \tan (θ) |

Also we then have

α_{2} = \sec (θ) + | \tan (θ) |

and

β_{2} = - \sec (θ) + | \tan (θ) |

α_{1} + β_{2} = 2 | \tan (θ) | = - 2 \tan (θ)

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

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