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  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise

Transcript

Example 22 Solve tan 2x = – cot (x" + " πœ‹/3) tan 2x = –cot (π‘₯" + " πœ‹/3) We need to make both in terms of tan Rough tan (90Β° + ΞΈ) = –cot ΞΈ –cot ΞΈ = tan (90Β° + ΞΈ) –cot ΞΈ = tan (πœ‹/2 " + ΞΈ" ) Replacing ΞΈ by x + πœ‹/3 –cot ("x + " πœ‹/3) = tan (πœ‹/2 "+ x +" πœ‹/3) tan 2x = tan (πœ‹/2+x" + " πœ‹/3) tan 2x = tan (πœ‹/2 " + " πœ‹/3 " + x" ) tan 2x = tan ((3πœ‹ + 2πœ‹)/(2 Γ— 3) " + x" ) tan 2x = tan (5πœ‹/6 " + x" ) General solution Let tan x = tan y tan 2x = tan 2y From (1) and (2) tan 2y = tan (5πœ‹/6 " + x" ) 2y = 5πœ‹/6 + x General solution is 2x = nΟ€ + 2y where n ∈ Z Put 2y = ("x + " 5πœ‹/6) 2x = nΟ€ + ("x + " 5πœ‹/6) 2x – x = nΟ€ + 5πœ‹/6 x = nΟ€ + πŸ“π…/πŸ” where n ∈ Z

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.