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Example 22 - Solve tan 2x = - cot (x + pi/3) - Class 11 - Finding general solutions

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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Example 22 Solve tan 2x = โ€“ cot (x" + " ๐œ‹/3) tan 2x = โ€“ cot (x" + " ๐œ‹/3) We need to make both in terms of tan tan 2x = tan (๐œ‹/2+x" + " ๐œ‹/3) tan 2x = tan (๐œ‹/2 " + " ๐œ‹/3 " + x" ) tan 2x = tan ((3๐œ‹ + 2๐œ‹)/(2 ร— 3) " + x" ) tan 2x = tan (5๐œ‹/6 " + x" ) General solution tan x = tan y โ‡’ tan 2x = tan 2y From (1) and (2) tan 2y = tan (5๐œ‹/6 " + x" ) โ‡’ 2y = 5๐œ‹/6 + x General solution is 2x = nฯ€ + 2y where n โˆˆ Z put 2y = ("x + " 5๐œ‹/6) 2x = nฯ€ + (x + 5๐œ‹/6) 2x โ€“ x = nฯ€ + 5๐œ‹/6 Hence, x = nฯ€ + 5๐œ‹/6 where n โˆˆ Z

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