Example 26 - Prove cos 2x cos x/2 - cos 3x cos 9x/2 = sin 5x - 2 sin x sin y formula

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

Transcript

Example 26 Prove that cos 2x cos /2 cos 3x cos 9 /2 = sin 5x sin 5 /2 Taking L.H.S Now, cos 2x cos /2 cos 3x cos 9 /2 Putting values = 1/2 ("cos " (5x/2)" + cos " (3x/2)) 1/2 ("cos " (15 /2)" + cos " (( 3 )/2)) = 1/2 ("cos " (5x/2)" + cos " (3x/2)) 1/2 ("cos " (15 /2)" + cos " (3 /2)) = 1/2 ("cos " (5x/2)" + cos " (3x/2)" cos " (15 /2)" cos " (3 /2)) = 1/2 ("cos " (5x/2)" cos " (15 /2)"+ cos " (3x/2)" cos " (3 /2)) = 1/2 ("cos " (5x/2)" cos " (15 /2)"+ " 0) = 1/2 ("cos " (5x/2)" cos " (15 /2)) = 1/2 (" 2 sin " ((5 /2 +15/2 )/2)" . sin " ((5 /2 15/2 )/2)) = 1/2 (" 2 sin " ((5 + 15 )/(2 2))" . sin " ((5 15 )/(2 2))) = 1/2 (" 2 sin " (20 /4)" . sin " (( 10 )/4)) = 1/2 (" 2 sin " (5 )" . sin " (( 5 )/2)) = 1/2 (" 2 sin " (5 )" " ( "sin " (( 5 )/2))) = 1/2 ("2 sin " (5 )" sin " (( 5 )/2)) = sin (5 ) sin (( 5 )/2) = R.H.S Hence L.H.S. = R.H.S. Hence proved

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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.