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  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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Example 23 Solve sin 2x โ€“ sin 4x + sin 6x = 0. sin 2x โ€“ sin 4x + sin 6x = 0 (sin 6x + sin 2x) โ€“ sin 4x = 0 2 sin ((6๐‘ฅ + 2๐‘ฅ)/2) cos ((6๐‘ฅ โˆ’ 2๐‘ฅ)/2) โ€“ sin 4x = 0 2 sin (8๐‘ฅ/2) cos (4๐‘ฅ/2) โ€“ sin 4x = 0 2 sin 4x cos (2x) โ€“ sin 4x = 0 sin 4x (2 cos (2x) โ€“ 1) = 0 Hence sin 4x = 0 or 2cos 2x โ€“ 1 = 0 sin 4x = 0 or 2cos 2x = 1 sin 4x = 0 or cos 2x = 1/2 We need to find general solution both separately General solution for sin 4x = 0 Let sin x = sin y โ‡’ sin 4x = sin 4y Given sin 4x = 0 From (1) and (2) sin 4y = 0 sin 4y = sin (0) 4y = 0 โ‡’ y = 0 General solution for sin 4x = sin 4y is 4x = nฯ€ ยฑ (-1)n 4y where n โˆˆ Z Put y = 0 4x = nฯ€ ยฑ (-1)n 0 4x = nฯ€ x = ๐‘›๐œ‹/4 where n โˆˆ Z General solution for cos 2x = ๐Ÿ/๐Ÿ Let cos x = cos y โ‡’ cos 2x = cos 2y Given cos 2x = 1/2 From (3) and (4) cos 2y = 1/2 cos (2y) = cos (๐œ‹/3) โ‡’ 2y = ๐œ‹/3 General solution for cos 2x = cos 2y is 2x = 2nฯ€ ยฑ 2y where n โˆˆ Z putting 2y = ๐œ‹/3 2x = nฯ€ ยฑ ๐œ‹/3 x = 1/2 (2nฯ€ ยฑ ๐œ‹/3) x =2๐‘›๐œ‹/2 ยฑ 1/2 ร— ๐œ‹/3 x = nฯ€ ยฑ ๐œ‹/6 where n โˆˆ Z Hence General Solution is For sin4x = 0, x = ๐‘›๐œ‹/4 and for cos 2x = 1/2 , x = nฯ€ ยฑ ๐œ‹/6 where n โˆˆ Z

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