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Question
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`.
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