Maharashtra State BoardHSC Arts 12th Board Exam
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Find the principal solutions of tan x = -3 - Mathematics and Statistics

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Sum

Find the principal solutions of tan x = `-sqrt(3)`

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Solution

tan x = `-sqrt(3)`

∴ tan x = `-tan (pi/3)`

∴ tan x = `tan (pi - pi/3)`

= `tan ((2pi)/3)` and  tan x = `tan (2pi - pi/3)`

= `tan ((5pi)/3)`

such that `0 ≤ (2pi)/3 < 2pi` and `0 ≤ (5pi)/3 < 2pi`

∴ The required principal solutions are x = `(2pi)/3` and x = `(5pi)/3`.

Concept: Trigonometric Equations and Their Solutions
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