Subscribe to our Youtube Channel - https://www.youtube.com/channel/UCZBx269Tl5Os5NHlSbVX4Kg

Slide32.JPG

Slide33.JPG
Slide34.JPG Ex 3.4.jpg Slide36.JPG

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

Transcript

Ex 3.4, 9 Find the general solution of the equation sin x + sin3x + sin5x = 0 sin x + sin 3x + sin 5x = 0 (sin x + sin 5x) + sin 3x =0 (sin x + sin 5x) + sin 3x = 0 2 sin ((๐‘ฅ + 5๐‘ฅ)/2) . cos ((๐‘ฅ โˆ’ 5๐‘ฅ)/2) + sin 3x = 0 2 sin (6๐‘ฅ/2) . cos ((โˆ’4๐‘ฅ)/2) + sin 3x = 0 2 sin (3x) . cos (โˆ’2x) + sin 3x = 0 We know that sin x + sin y = 2sin ((๐‘ฅ + ๐‘ฆ)/2) cos ((๐‘ฅ โˆ’ ๐‘ฆ)/2) Replacing x by x & y by 5x 2 sin 3x . cos 2x + sin 3x = 0 sin 3x (2cos 2x + 1) = 0 Hence We need to find general solution both separately General solution for sin 3x = 0 Given sin 3x = 0 sin 3x = 0 2cos 2x + 1 = 0 2cos 2x = โ€“1 cos 2x = (โˆ’1)/2 General solution is 3x = nฯ€ x = (๐‘›๐œ‹ )/3 where n โˆˆ Z General solution for cos 2x = (โˆ’๐Ÿ)/๐Ÿ Let cos x = cos y cos 2x = cos 2y Given cos 2x = (โˆ’1)/2 From (1) and (2) cos 2y = (โˆ’1)/2 cos 2y = (โˆ’1)/2 cos (2y) = cos (2๐œ‹/3) 2y = 2๐œ‹/3 General solution for cos 2x = cos 2y is 2x = 2nฯ€ ยฑ 2y Putting 2y = 2๐œ‹/3 2x = nฯ€ ยฑ 2๐œ‹/3 Rough We know that cos 60ยฐ = 1/2 But we need (โˆ’1)/2 So, angle is in 2nd and 3rd quadrant ฮธ = 60ยฐ 180 โ€“ ฮธ = 180 โ€“ 60 = 120ยฐ = 120 ร— ๐œ‹/180 = 2๐œ‹/3 x = 1/2 (2nฯ€ ยฑ 2๐œ‹/3) x = nฯ€ ยฑ ๐œ‹/3 where n โˆˆ Z Hence General Solution is For sin3x = 0, x = ๐’๐…/๐Ÿ‘ OR For cos 2x = (โˆ’1)/2 , x = nฯ€ ยฑ ๐…/๐Ÿ‘ where n โˆˆ Z

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.