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

Transcript

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 โ 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 โ Z Put y = 0 4x = nฯ ยฑ (-1)n 0 4x = nฯ x = ๐๐/4 where n โ Z General solution for cos 2x = ๐/๐ 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/3) โ 2y = ๐/3 General solution for cos 2x = cos 2y is 2x = 2nฯ ยฑ 2y where n โ Z putting 2y = ๐/3 2x = nฯ ยฑ ๐/3 x = 1/2 (2nฯ ยฑ ๐/3) x =2๐๐/2 ยฑ 1/2 ร ๐/3 x = nฯ ยฑ ๐/6 where n โ Z Hence General Solution is For sin4x = 0, x = ๐๐/4 and for cos 2x = 1/2 , x = nฯ ยฑ ๐/6 where n โ Z