Ex 3.4, 1 - tan x = root 3. Find principal and general solution - Finding general solutions

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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Ex 3.4, 1 Find the principal and general solutions of the equation tan x = √3 tan x = √3 We known that tan 60° = √3 Here tan x is positive tan is positive in Ist and IIIrd quadrant Value in Ist quadrant = 60° Value in lllrd Quadrant = 180° + 60° = 240° So principal Solutions are x = 60° and x = 240° x = 60 × 𝜋/180 and x = 240 × 𝜋/180 x = 𝜋/3 and x = 4/3 𝜋 Now we find general solution Assuming tan x = tan y also tan x = √3 Form (1) and (2) tan y = √3 tan y = tan 𝜋/3 ⇒ y = 𝜋/3 Since tan x = tan y General Solution is x = nπ + y where n ∈ Z Put x = 𝜋/3 Hence, x = nπ + 𝜋/3 where n ∈ Z

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