Question 1 - Principal and General Solutions - Chapter 3 Class 11 Trigonometric Functions

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Question 1 Find the principal and general solutions of the equation tan 𝑥 = √3 Given tan 𝑥 = √3 Principal Solution Principal solution is when 0 ≤ x ≤ 2𝜋 We know that tan 𝛑/𝟑 = √3 & tan (𝟒𝛑/𝟑) = tan (π" + " π/3) Therefore, the principal solutions are 𝑥 = 𝛑/𝟑 and 𝟒𝛑/𝟑 . General Solution Given tan 𝑥 = √3 tan 𝑥 = tan π/3 ∴ 𝑥 = n𝛑 + 𝛑/𝟑, where n ∈ Z Therefore, the general solution is 𝑥 = nπ + π/3 , where n ∈ Z