Question
Download Solution PDFWhat is the principal solutions of the equation \(\tan x=-\frac{1}{\sqrt{3}}\)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The principal solutions of a trigonometric equation are those solutions that lie between 0 and 2π.
Formula:
General solution of tan(x) = tan(α) is given as;
x = nπ + α where α ∈ (-π/2 , π/2) and n ∈ Z.
Calculation:
Given, \(\tan x=-\frac{1}{\sqrt{3}}\)
⇒ tan(x) = tan(-π/6)
∴ α = -π/6
⇒ x = nπ + (-π/6) , n ∈ Z
Putting n = 1 and 2, we get -
x = 5π/6 and 11π/6
Last updated on May 26, 2025
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