Learn All Concepts of Chapter 2 Class 11 Relations and Function - FREE. Check - Trigonometry Class 11 - All Concepts

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

Transcript

Example 22 Solve tan 2x = โ€“ cot (x" + " ๐œ‹/3) tan 2x = โ€“cot (๐‘ฅ" + " ๐œ‹/3) We need to make both in terms of tan Rough tan (90ยฐ + ฮธ) = โ€“cot ฮธ โ€“cot ฮธ = tan (90ยฐ + ฮธ) โ€“cot ฮธ = tan (๐œ‹/2 " + ฮธ" ) Replacing ฮธ by x + ๐œ‹/3 โ€“cot ("x + " ๐œ‹/3) = tan (๐œ‹/2 "+ x +" ๐œ‹/3) 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 Let tan x = tan y tan 2x = tan 2y From (1) and (2) tan 2y = tan (5๐œ‹/6 " + x" ) 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 x = nฯ€ + ๐Ÿ“๐…/๐Ÿ” where n โˆˆ Z

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