Question 5 - Examples - Chapter 3 Class 11 Trigonometric Functions

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Example 22 - Solve tan 2x = - cot (x+pi/3) - Teachoo - Examples

Example 22 - Chapter 3 Class 11 Trigonometric Functions - Part 2
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Question 5 Solve tan 2x = – cot (x" + " 𝜋/3) tan 2x = –cot (𝑥" + " 𝜋/3) We need to make both in terms of tan Rough tan (90° + θ) = –cot θ –cot θ = tan (90° + θ) –cot θ = tan (𝜋/2 " + θ" ) Replacing θ by x + 𝜋/3 –cot ("x + " 𝜋/3) = tan (𝜋/2 "+ x +" 𝜋/3) tan 2x = tan (𝜋/2+x" + " 𝜋/3) tan 2x = tan (𝜋/2 " + " 𝜋/3 " + x" ) tan 2x = tan ((3𝜋 + 2𝜋)/(2 × 3) " + x" ) tan 2x = tan (5𝜋/6 " + x" ) General solution Let tan x = tan y tan 2x = tan 2y From (1) and (2) tan 2y = tan (5𝜋/6 " + x" ) 2y = 5𝜋/6 + x General solution is 2x = nπ + 2y where n ∈ Z Put 2y = ("x + " 5𝜋/6) 2x = nπ + ("x + " 5𝜋/6) 2x – x = nπ + 5𝜋/6 x = nπ + 𝟓𝝅/𝟔 where n ∈ Z

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo